One of my friends mom is a judge for the Foundation Quarter Horse Registry.
She does have a rather sweet face, I think she is flat adorable, but from the side she has the profile shape of a belgian lol.
If you don't mind, please elaborate what you mean on her conformation?
I wouldn't lunge with draw reins or even side reins. Sometimes they can make matters worse by making the neck build muscle in the wrong places or break the natural arch of the neck, especially when applied incorrectly.