Yes, laneyba, as sammi said, the fact that you're still living at home won't bar you from One Parent Family Payment. If you're available for work, you may be eligible for jobseeker's benefit (if you worked recently).
You should be seeking maintenance from your partner as he is liable to maintain his child.
If you have no income while waiting on your SW claim, you can apply for Supplementary Welfare Allowance, which is administered by Dept of Social Protection staff who are generally based at your local Health Centre. It's a means-tested payment, and anything you are paid will be taken from the arrears of your One Parent Family Payment (or Jobseeker's, if you qualify).