Claim DLA for your child, and tell the nursery that you will be applying for DLA, and ask them to help you evidence all of the ways that your child is developmentally different from other children, requiring more care.
Non-verbal autism (whilst still hard to claim for) is quite easy to document. It can come under the SMI criteria as well as the VUW criteria if they cannot follow instructions for their own safety, needing restraint like holding hands, carrying, or requiring a pushchair when out in public
If she wakes in the night you need to start documenting that now, frequency, when she goes to sleep, when she wakes up, and why you need to be awake with her. Make nursery aware every single time if she's had poor sleep so that they can also verify that she has nightly care needs too.
There is no age limit to claim DLA, so even at her young age you absolutely can.
This money needs paying to you. You can use this money to appropriately house your child, meaning it can go towards household costs and bills if that is what's needed, as it also covers the gap in earnings because it is well known parents of disabled children often have to reduce or give up work completely.
Then, claim carers allowance, as well as universal credit, and let them know you're separating from an abusive man, make sure that you get the child element as well as the disabled child element.
If you're not married and the house is in his name, that doesn't necessarily mean that you won't get anything out of the house if you can evidence you've contributed to the sale of the house or put any money towards renovations, however you will need to speak to a solicitor about this, and that will ultimately cost money so it depends how much you've spent, but you might be able to get half an hour free to discuss whether it's possible to recoup any costs from your partner or whether you want to just see it as spoils of war and let it go.
Speak to womens aid too, as well as IDAS. IDAS can help do a risk assessment for you, they will then take your case to a MARAC meeting, basically a multidisciplinary meeting, where you're assessed to see whether you can have priority social housing, you might need to make a social housing application first, but they'll discuss this with you. - I will say that IDAS are extremely helpful, however they're not always fantastic at contacting you back, so you may have to keep contacting them and being pro-active if they're not calling you when they say they will. This is from my own experience and experience supporting a friend leaving an abusive situation. They might ask you if you're able to move to temporary accomodation, and in your circumstances, I would do absolutely everything possible to go ahead with that.
If he is your childs father, make sure you go through CMS for child maintenance too.