Honestly everyone telling OP that she isn't cut out to be a stepmum is being really OTT. Planning a life together, having a plan for how that will work out, that is a whole process if you are taking it seriously. Loads of us do not want to live our lives in some kind of serendipitous "oh look the stork landed a 6 yr old in my lap, this is my life now!" way.
OP's partner has dropped his child, FULL TIME IN HER HOUSE, no school no regular schedule, just "here, I, me, the big I AM have decided I am having my son full time now, which OF COURSE means the woman in my life must also immediately accept this massive change. Never mind that this isn't my house nd she's currently doing me a favour my letting me stay."
Your 'partner' needs to find his own place ASAP. This is far too much, too soon. If he wants to get his autistic son settled, find him a school and get his support network in place, that's lovely. He needs to go and do that, though, and stop expecting you to pick up his slack.
And yes, I have an autistic son, husband, and I work with autistic children. I am appalled at this father's behaviour, unless there's some drip feed about him rescuing this child from an abusive situation. Even then, he needs to take charge, get his own place, and start building a home where his son will feel safe.