I am not a specialist, so take my words in that light.
I have heard of a study saying that the rate of those with autism and Aspergers that have gender dysphoria is greater than in the general population. Aspergers is something I am personally familiar with in those I love, though the people close to me are quite "high functioning." From my lay reading of science research, exposure to various hormones in the womb during critical times of fetal development, are suspected, though not proven, factors in both the development of ASD and ->-bleeped-<-. My lay opinion is that I wouldn't be surprised if their increased rates had more to do with this, than with anything like people becoming confused that they are transgender because of a misplaced intense obsession. From my experience with both the Aspergers and transgender loved ones I have in my life, it just seems like this is not likely. It may be likely that if someone is transgender and also Aspergers, that they may become more intensely obsessed with their transition going "just right." This could make it harder on them, possibly, without proper support. A professional councilor who specializes in and has plenty of experience with gender dysphoria in general, and more specifically those with both Aspergers and gender dysphoria, would be ideal in helping you both. Do research and see if you can get people to recommend or get you in contact with a therapist that has such experience, even if they are outside your area. You want to talk to such an expert, and then they can help you know what to look for in finding the right help for your child in your area. Try to get recommendations from within the trans* community. Maybe even Cindy could get you in touch with the clinic she mentions, and they might be able to help direct you?
But please heed Cindy's warning about finding the right therapist. There are plenty without the proper understanding of gender dysphoria that can (and often do) more harm than good. If anyone tries to invalidate your child's proclaimed gender identity by saying it is caused by something else, like Aspergers, I would be very cautious and seek the opinion of another specialist with broad experience with gender dysphoria. There has been a long history of transgender individuals having their identity invalidated and pathologized, and it is very harmful for a transgender individual to go through that.
On a personal note, I am so happy to see you, a mother, advocating like you are for your child. Your love and determination to find the help you both need will be such a gift in your child's life.
Keep us updated on your journey, and please feel fee to continue to ask questions and seek help from the people in this community, and help others by sharing your experience. We gain so much from having this support from one another.
Hugs,
Felice