Without making any comment on whether "the rules" are right or wrong, the Prince Charlie is technically for black tie wear. For white tie, you'd need a doublet - either the regulation doublet, which looks like a Prince Charlie but with inverness flaps, or a Sheffmuir, Montrose, etc.

My personal opinion is that I am not a fan of the regulation doublet, and I think that a Prince Charlie with a white vest and tie would look quite nice.