YES, change your doctor, maybe consider switching to an opthamologist. Even more than that, however, make sure you can get advice from a doctor who specializes in contacts and testing the fit.
I have astigmatism too (although my doctor says it's slowly correcting itself), and they do make special contacts just for it. Depending on how severe your DD's is, you may want to consider them. It's possible that because she's new to contacts, the doctor wanted to try her with different types before settling. While there might be a slight difference in her vision with contacts vs. glasses, she got contacts so that she could see, the same reason she was wearing glasses...if her vision is still too impaired to comfortably see the board in her classroom, the contacts aren't working.
I was diagnosed with Thygeson's Disease last fall (it's a looooooong story), and part of the reason I may have developed it is because of ill-fitting contacts. They don't really know for sure. I went through several doctors who weren't doing much to help me, and I ended up, finally, at my mom's optometrist. He explained that his specialty is contacts, unlike several of his colleagues that I had visited, including an opthalmologist. Unfortunately, none of THEM admitted that there may be people who knew more than they did about the subject, so it took a while for me to end up with him. The good news, however, is that he worked with me and gave me many samples of contacts to try because of my condition until he found one that fit well.
If your DD's doctor is not willing to try different brands, models, and prescriptions, you need to find someone who will. Trust me...once she finds a contact that fits her needs, her vision will improve, her eyes will be comfortable, and astigmatism won't be an issue at all.
Good luck!
ETA: Sorry, my reply took a little longer to type than I expected, so I'm a little late with the advice...hope I don't confuse you! Just do what you feel comfortable with!!