You should call into your local social welfare office as soon as possible and discuss a claim with the people there. You may be due a payment if you are available for work. If you feel you are unavailable for work, you may be able to sign on for credits, please check with the people in social welfare as credits are important for your future PRSI pension rights. I take it that since you have a small baby you're not actually looking for work, otherwise you'd have gone back to your old job.
The people to speak with about rent allowance are your local health board staff. With anyone you're always better going directly to the people involved such as social welfare or the health board as they will look at your case on an individual basis and help you as appropriate.
If your husband is working and you're not, he will be able to take over your tax free allowance/tax credits, again he should contact the tax people in Northern Ireland if his employer is based there and paying NI tax. This should make a difference to his take home pay.
Hope this helps...good luck!