Yes, I am aware they're called Long dragons for a reason (I know that's now what Long means in Chinese, just making a pun) but if she's not fully grown perhaps she hasn't developed the serpentine body needed for magical flight.
Also, there are some lizards that swim that way too, so having arms and legs does not necessarily mean an animal uses them all the time.
I think in the end it is going to be that the whole grass is greener on the other side idea. Whimsey is going to think no one cares and runs away from home. The other dragons are going to come looking for her and rampage until she goes home and sees she is really truly loved by other dragons