I've worked as a nanny in the past and want to pursue it, though it's tough to find a good match with a family because I think a lot of potential employers think I seem a bit strange.
Can you practice your interviewing skills with a friend? How well you connect and can communicate with a potential nanny employer is huge. Eye contact, smiling, and reacting appropriately to questions and conversation is really important. Try not to fixate on details. I have many ASD friends and coworkers. Its very apparent once you get to know them but they have learned enough social skills to get by. They can handle casual conversation and interviews well but they are much older and have had more practice over time. The key is to realize that what just comes naturally for other people needs to be a learned behavior for you and it is harder for you. However, you have to keep working on getting it.
You really can't say I may seem strange because I has ASD because honestly that may be true OR you may actually be strange and have ASD. The employer is going to make a decision based on what you present to them regardless of why you presenting this way.