What does "reasonably quickly" mean? When making a suggestion, you need to avoid or better define vague terms like this; it's okay if you aren't really sure where to put the numbers (even analogies to similar things will work, like "50% faster than furnace minecarts"), we can hash that out in the resulting discussions as different points are brought up.
You should also provide some options for things like fuel. We have the coal item, sure, but we can compress 9 of those into a coal block so would a coal block result in 9 times the duration? What about blaze rods or lava buckets (they're a furnace fuel, though the much older furnace minecarts aren't yet updated to use anything but coal items)?
It's not part of the original suggestion, but what would happen if the player let loose an elytra rocket while in the airship? Would it just shoot upwards like fireworks normally do or would it act as a booster like with elytra? This sort of peripheral scenario will be brought up by the average player who is already exposed to similar mechanics (ie, elytra) so it's probably a good idea to consider such things--even if it's only going to be a silly easter egg.
Another thing might be to figure out a problem with a similar mechanic that your suggestion is intended to fix or mitigate. This airship, at the cost of being relatively slow, could give you more control than an elytra during flight, making it a better mode for doing sky-high builds or sniping targets or whatever.