If you can explain why the child must wait outside of the normal queue environment, you can request a
DAS from Guest Relations inside the first Park you visit on your trip; you only need to get it once per trip, and it will work at all of the parks for the rest of your trip. The DAS offers no benefit outside the Parks (for example at Disney Springs or the Resort hotels).
Doctor's notes are not accepted, and CMs don't want to/can't really accept diagnoses; for example saying "I need a DAS because I (or my family member) have <insert disease/condition name here>" won't help. You have to be able to explain why waiting outside the "regular" queue is helpful.
Not everyone is well-served by the DAS; for example, my condition isn't really helped by using a DAS... rather I choose to use a personal mobility device because that is the best possible solution for me.
Depending on the age of the person, children may also be eligible for a "stroller as a wheelchair" tag, however, again, just like with the DAS, the CM will need to know why that accomodation is helpful to the persons' experience.
Many families here employ a lot of different strategies - everything from hoodies and dark glasses, with hearing protection, to bringing along a tablet or other device to help with distraction. Some kids do better riding in a stroller or wheelchair (sometimes with a blanket draped over to create a personal space).
Here's just one thread I found (using the "Search" magnifying glass on the top right of the main DISabilities landing page) that might be helpful:
Need reassurance - child with autism