The film's co-Directors toyed with the idea of making Dragon into a pegasus but ultimately decided against it because it didn't really add anything to the film to see her transform.
Quoting from the Director's Audio Commentary (between co-directors Kelly Asbury and Conrad Vernon):
We worked on that a loooong time. I mean, how do we show that that potion affects Fiona as well as Shrek? I mean yeah, big blue flash, yeah one flash. I think there was one point, because Donkey was, Donkey changes into a "noble steed", everyone asks, yeah but we asked ourselves, everyone asked us afterward, 'Who does Dragon change into?'
Right
And at one point we did have her change into a Pegasus, a biiig pink horsie with wings ... and I still think offscreen, she's a pegasus somewhere right now, wondering what the heck's going on and flying around...and then she changes back into a dragon before the end of the movie.
And from the film's Second Audio Commentary (between Producer Aron Warner and editor Michael Andrews):
Someone asked me "what about the Dragon, how come you don't see her transform" and I said "funnily enough, we did do that at one point...but it was just a bit weird to suddenly jump back to the Dragon".
Well yeah, at one point the Dragon was a unicorn or a pegasus with wings.
Yeah, she was part of the 'Rescue Team' later in the film but she looked too much like a pretty pony which was fine but it ended up just not hitting me...