Hi hun,
Sorry to hear that but at least it's all amicable......sometimes you just have to do what feels right for all of you!
You would need to inform Child Benefit as you would be entitled to a slightly higher rate and they will send you a letter confirming this. Also, let tax credits know - think you may be entitled to more child tax credits but not sure. Once you've done this, contact your local council for forms regarding housing benefit (now called Local Housing Allowance) and Council Tax Benefit.....hopefully, by the time the forms for those come through, you should have letters from tax creds & child ben as you will need them for proof of ur incomings.
How many bedrooms does ur house have? As a single parent with one child, ur entitled to rent help for a 2 bedroom property (regardless of what size - they base it on bedrooms per person/couple now) which is about ??150 a week currently. Check this site out https://lha-direct.therentservice.gov.uk/Secure/Default.aspx it will have info on there.