Well There are a bunch of moogle types already, as seen in the primal fight, so why not.
_EDIT_ not summoned as a mount
They could have the same style of levelling as the chocobo.
(healer, dps, or tank)
There are other things they can do with them as well, like use the same systems they use for bardings. (change head and body gear)
Or it can be set, like you must choose one of the preset moogles, to become your companion.
Either way, I believe a lot of player would love to run around with their moogle companion.
P.S. I think a bard moogle would be my choice, you guys?