Is a bag an appropriate b-day gift

I think you are really sweet for even thinking of a Bal for your niece -

but even if she takes perfect care of her things and treasures them, as I'm sure she would, my main objection would be for her - where would she go from there? what would she look forward to? maybe for her 21st, but even then, these tend to be the kinds of things that are most meaningful when bought yourself with money you earned...
 
I think that each age should have its appropriate joys.
I believe that life is funnier if you always have new aims and probably she would appreciate much more a designer's handbag when she'll be 18 or after (when she will be studying and won't be able to buy many designers' iems by herself). An accessory or a less expensive brand of handbags would be appropriate, IMO