I don't disagree with the ideas so far of trying to find out not only how warplanes could be useful against Leviathans but also when in the timeline. There are some problems that need to be delt with however.
The first obvious one is location. Planes have limited range so usually airfields were possitioned defensively around where the enemy was thought to come or offensively the planes would need to be carried to their location. This made sense as the enemy could only come from certain locations but with Leviathans an invading fleet could come from anywhere and simply bipass any defensive locations of the enemy. It wouldn't be easy for you, for example, to spot an enemy fleet and just scramble air fighters to that location.
Elevation is the most tricky one. Airplanes were slightly to moderately effective in the era of around 1915-1918 but only against targets lower than they were. 10-20,000 ft would be an interesting benchmark because this would be the altitude crewman on Leviathans would start to feel the effect of the cold and oxygen depletion inherant at this altitude (IE it's safe to assume that until airsuits or pressurization was invented [the Germans first tested this in 1931] Leviathans wouldn't travel much higher than this.) Aircraft were less prone to this risk since you only needed to protect 1 or, rarely, 2 pilots and they would only be at higher altitudes for very short periods of time if at all. Still, at 1915 the highest recorded altitude for a plane was around 12,000 ft and by 1920 only 33,000. An airplanes effectiveness against a target at the same level or higher would be greatly diminished with machine guns and bombs so at the very least airplanes as an effective weapon against Leviathans would be sometime after 1915, when they could get higher. Airmasks in planes were also not used until well after WWI (developed first primarily by the Russians).
The third, already mentioned, is weaponry. Airplanes were effective against zeppelins as early as 1915 but only for 2 reasons. They were able to get higher than the zeppelin and the zeppelin was a relatively fragile craft. Neither would be true for fighters against Leviathans. Furthermore, while strafing took place against ground troups around 1915-18, it wasn't really used against ships and their crews until WWII, famously 1941 and the attack on Pearl Harbor. You can probably assume that figher pilots in the Leviathan universe wouldn't be honing their skill of picking off the deck crews of the Leviathans until somewhere between these two dates.
As a side note, it would be interesting to see what role zeppelins in this era take, if at all. Reading the Leviathan timeline as per the website, it looks like there is a period where the Germans aren't really pursuing Leviathan development and perhaps at this time they are still able to carry out a few zeppelin bombings. Leviathans would absolutely be zero match for Leviathans in any sort of combat however, but they may still be useful as some sort of "supplier" and gas, food and munitions are still needed and if you can get those to a Leviathan via a zeppelin that would mean they would not have to land making them less vulnerable (the Germans would obvioulsy be best at this, a possible race trait to go with their fleet?)
Bombs were an early-era plane's most useful weapon against big targets however bombs dropped by planes were in the 2-5 kg range for a long time (Japanese kept 2 kg bombs until around the beginning of WWII) and there were not many recorded incidents of airplanes attacking ships and even then there were no recorded hits again until around WWII.
However, since destroyers in Levianthans have "torpedoes" we could assume planes could use this same technology provided they could carry it, and then it would also be okay for them to have the same elevation. To do so would require a type of "heavy bomber" and those didn't come onto the scene until around 1917-18 or so (no idea how the makers of Leviathans explain torpedo use in the air, propulsion for torpedoes in this era was some type of compressed gas or ignited liquid. This was ideal with the resistance and near-weighlessness water offered but wouldn't work in the air). Torpedo planes seem like they would be the best option and would make the to-game conversion very easy... just roll like you would for the other torpedoes.
Again with heavier planes requiring to be closer to some sort of airbase, carriers would almost be cruicial for any sort of practical usefullness against a Leviathan. Which is actually good news. The first carriers were on scene, by the British no less, around 1918 and were gaining popularity around the mid 1920's. In our timeline carriers were only moderately useful during WWI because planes were only moderately useful and nations like the US didn't really buy into the idea (and only as a sort of fluke) until right before WWII (before this the battleship was king). But with a heavier presence in the air and a larger scale, potentionally longer conflict, carriers may have become more prevelently used earlier.
I would say Carrier Leviathans would be no different and we should be able to see Torpedo-carrying planes hunting down Leviathans around 1920 in their timeline with relative ease. Due to the economies of the nations in this era, the Japanese were the ones who most used and tested Torpedoes. Might this be the Japanese's fleets specialty when they are released?
As a reference timeline:
1910 The first recorded plane to take off from a "carrier" warship, though the plane was little more than a Wright's Brothers type lighcraft
1911 Italian airplane first used "bombs" against Turkish ground forces
this was roughly 2 kg, or about as much as you would use to help clear a tree stump from your backyard
1913 The Greeks used bombs against a Turkish naval fleet, no hits were scored
1914 A plane shoots another plane down with a handgun, (should show the fragility of aircraft at this point)
1914 the first successful land strike by an air force launched from a carrier by the Japanese
1914 First recorded kill with a machine gun attached to a French plane gunned down a German plane (Lewis gun, machine guns on airplanes probably were not tremendously useful before this. Strafing introduced as a concept not too long after this using the Avro 504)
1915 British airplane took down the first zeppelin from above with 6 bombs
1916 airplanes became increasingly effective against zeppelins through use of incendiary rounds which would pierce the tough outer skin and set the zeppelin on fire (Germans initially countered this by making zeppelins fly higher, 20,000 ft where airplanes could not yet reach but by 1918 the British already had airplanes capable of reaching those altitudes)
1917 Sopwith Cuckoo first US plane to test drop aereal torpedo
1918 First flat top carrier, HMS Argus, also dubbed "first carrier capable of launching and landing naval aircraft." This is key as before most of the planes "launched" from a carrier might have been a lighter craft or else a seaplane lowered and lifted from the sea by a crane (obviously impossible to do from a Leviathan.)
1918 English use the HMS Furious in a successful aircraft carrier strike against German Zeppelin hangars (finally a traditional biplane design launched from a carrier)
1921 US non-war demonstration of the ability of heavy bomb aircraft to sink battleships.
