IPSEA is a charity that can help with legal advice or the Childrens Legal Centre.
You need to apply for a statement. Download and get a free hard copy of the SEN Code of Practice. There is info in there about young children with severe and complex needs only needing one overarching report and also about emergency placements.
I don't know what dx you are expecting but you can look at local special schools and can also look at private schools or ABA (not just for autism also for behaviour issues).
There are lots of Acts eg Childcare Act, Equality Act which bang on about right to childcare for a disabled child / rights as a carer. You could also contact disabled childrens team at social services and ask for a carers assessment for you and a disabled child assessment. Also alert your MP
Contact Parent Partnership for info they are not always that fantastic or that independent of council but should be ok in an exclusion situation. You can appeal exclusion from school. Info on IPSEA website about exclusions. I don't know if LA have to put in education as under 5 eg home tutor
If I were you I would be looking at any special schools or units including in the private sector.
You can take unpaid parental leave. You could then apply for DLA, Carers allowance and tax credits not what you want but you may as well get the applications off just in case.
You should put in writing to the SEN officer at the council the need for an urgent placement due to you being at risk of losing your job. That way if they take ages you can at least complain about it afterwards and try and get compensation.
If you have a local carers charity they often help you with DLA forms etc