Here are my 2cents on the subject:
Invisalign is not really a good idea for non-adults because the aligners are removable, which means your child has the opportunity to take them out and lose them, or just not wear them properly because they may become a nusance after the initial novelty wears off. It's hard enough to get your kid to keep track of a retainer that is only worn at night. Keeping track of aligners that are worn 24/7 for a year or two could get complicated for even the most responsible child.
Invisalign is not recommended for people with complicated cases where extractions are needed or there are severe bite issues. There are many people who have posted on this board over the years who have started out with Invisalign and have ended up in traditional braces anyway. Some people who didn't have bite issues before Invisalign wound up having bite issues afterward.
Dentists and orthodontists make an investment in offering Invisalign to their patients. This doesn't mean that it is the best method for straightening the teeth. A good orthodontist will recognize this and NOT offer it when it is NOT appropriate. Also, understand that a dentist who has "been trained in Invisalign" may not have all the proper training in tooth movement and bite correction that an orthodontist does.
Please don't think that I'm totally anti-Invisalign -- I'm not. It does work for adults who need only MINOR corrections, under the supervision of an experienced ORTHODONTIST (not a dentist who "does braces.")
If I were you, I'd get 2 or 3 additional opinions. If your daughter and her orthodontist are dead set on Invisalign, you should find out what would happen if it wasn't working (if she kept losing the aligners or not wearing it properly). Would the orthodontist switch her to regular braces for no extra charge -- or would it cost you extra?
I'm the owner/admin of this site. Had ceramic uppers, metal lowers ~3 years in my early 40's. Now in Hawley retainers at night!