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...
As to why they didn't include her in the film until the very end, this is discussed in the film's second commentary. In short, it was because having a gigantic fire-breathing dragon as an ally instantly destroys any sense of suspense in the fim
We tried to put her in, several times before but... but you can't have her around a lot because she, 'cause she gets everything done. She can get through any obstacle.
Like we couldn't have her to get into the castle or anything like that, or to get those guys out of prison. It would have just made it all too easy.
