Benefits advise please

Hi there

Please can I ask for some advise.

I have always worked full time and am 37 years old.

I had a premature baby at the end of October and in 3 weeks time I drop down to statutory maternity pay which is £138 a week.

My partner is on a low income and earns about £138 a week.

I do not yet feel ready to leave my baby and go back to work.

Would I be entitled to housing benefit to top up my statutory maternity pay and my partners low income?

We will be bringing in approx £275 a week between us and the rent is £1000 a month. (2 bed house)

I plan to return to my job absolutely but would like to stay with my tiny baby til he is 6 or 7 months old.

I've never claimed anything before and don't know where to start.

I looked into tax credits but they base it on my last tax year and it seems I don't qualify.