ehm, yes you have a good point, but if she likes drawing so much, you could infuse the idea of Architectural Designs in her mind, and not worry about (ie. Starving Artists).... you know why im saying that... Architects are like Doctors. She having the drawing skills is a good start, that is one requirement, the other is Mathematics if she studies good id say go for a Architect University, yes takes 6 -7 years but man once she finished it. She be making in a month as you did your entire life.
atleast that is my point of view, as for her love for drawing stuff for fun as she does now, cause she thinks is cool and her Daddy is in the business. she can do it part-time and learn while doing it.
As a side note: i have a few Graphic designers friends in university all where so enthusiastic at beginning about it, then 2nd year came and they where thinking to drop from the school.
Its best to ask her where she sees herself in this business in next 10 years, and if she has stuff in her mind with being a artist, and im not saying the commercial type, but the more fancy and not understood types(ie. staving artists) ... that is going to be a rough future for her, if she tends in that direction.
plus she just finishes high-school, you can model her idea of designing, and help her choose a career point. where as a woman she needs to be in future, and can sustain herself, and not depend on her future husband or worry where her next freelancer job will come from.
im thinking at your problem, as i see myself if i wold have a daughter.
and from my point of view, not worth it getting into game industry as a graphic designer.
The text above is just my opinion on the issue posted by the OP no pwn intended or trolling.