I was in your position in August so I can tell you what I did if its any help.
Ring tax credits asap and cancel your joint claim and make a new one from the date of the split. That will automatically sort out NHS low income exception cards and you should get a letter from healthy start that you need to get signed by a heath visitor and send back and that will get the fruit/veg and vitamin vouchers for the little one sorted.
Ring Income support helpline and start a claim as soon as you can. They will register you, which gives you a start of claim date and send you a form which you need to fill in as quickly as you can and send back to them.
Ring the council and ask for a council tax benefit form, if you rent this is the same form as you will use to claim housing benefit. they told me they will pay council tax benefit from the Monday after the start of an income support claim and they'll back date if necessary but I'm guessing you need the money so get the form in as soon as you can.
If you have a mortgage you need to fill those details in on the income support form and they will send you another form about mortgage interest help.
My tax credits took less than a week and was done all over the phone, the income support took about a fortnight and the council tax benefits took about three weeks once I sent the form.
Good luck sorting all the paperwork but try and keep a list of date you apply so you can tick them off once they're sorted out.
Not sure if that's any help but good luck with it all 