IMHO, it becomes "whining" when the explicit or implicit premise is that the problem needs to be fixed by someone else correcting what they do. E.g., "a whiny liberal/conservative is one who blames conservatives/liberals for all of the country's problems".

I feel like with her gifts come a responsibility to make the most of them.

Be careful not to over-pressure her though. Kids who have been ridden eventually figure out how to opt out. (My father was a professor at a high-quality liberal arts college, and he noted that the second-highest dropout rate was second semester, senior year. The kids figured out that they could give their parents a fuck-you that was irrevocable.)