The value of the so-called "game design" schools are mostly hit or miss in terms of quality. Not just from school to school but semester to semester depending on who happens to be teaching (there's often a very high turnover rate) and the dedication and enthusiasm of the other students. The degree you exit with doesn't really have a lot of value other than it showing prospective employers that you can commit to and finish something you started. Students will typically come out of the program with some sort of finished class project and your contribution to it can be very beneficial if it's done well but it can also be a double-edged sword if you have classmates who are not as dedicated as you are. Group projects tend to only be as strong as their weakest link. Read books, get involved with online communities. The best way to show you can make games is to... make games. Simple puzzle and logic games are a great start, board games, card games, pen and paper RPGs, things like that. Good game design can be demonstrated in any media; some of the best designers I know started with or continue making non-digital games. Getting involved with the modding communities is a great next step. Modding an existing game lets you focus on the flow of design without having to worry about things like art and programming (although at least some basic knowledge of scripting languages can be very helpful and useful).
Good luck to your daughter. The industry needs more women.
All the best,