Even if this child was as young as 3, she may have been involved with or evaluated by a school district for services. I think it would be worth sending a detailed description to districts in the state- especially to their special education and developmental pre-school level programs. They could suggest informing school psychologists, OT's and PT's, just to see if the description of the child rings any bells. I also agree with others who have said that, even at her tiny size, she could have been as old as 7 or 8 (or even older). Severely handicapped children do move away from one area to another, but most of the folks who work with them- even for a short time- tend to remember the child, their unique combination of disabilities and needs. Perhaps asking districts to check their inactive files on students who never had records requested to be sent elsewhere?
I realize that is a long shot since the child may never have been engaged with a school district, but it would be much easier than trying medical records.
I'm thinking that the best likelihood of identifying this child is reaching out via media. Asking people to think if they had a neighbor or family member of this description who they have not seen since last year or longer. Perhaps the story was that the child was sent to live in a state facility, was at respite care, a camp, or even, sadly, died and was given no funeral. I think it's going to be someone who already thought a given story was hinky who will crack this case.
One last, also long-shot, idea... It is possible this child was being raised by a single parent alone. Are there any UID women located in the right time frame? What if a woman was murdered, the child was dumped, and she just sadly hasn't been reported missing? Unlikely, but may be worth ruling out....