You may be able to find a pro bono or free lawyer at your local bar association. Otherwise, yes you will need to hire and pay a lawyer. If your spouse has income your attorney may be able to file an emergency motion for in pendente relief - which is a fancy way of asking the court to force your spouse to pay for your attorneys fees.
Regarding your daughter, you and your spouse can agree upon custody issues. If you opt to litigate (which it doesn't sound like you financially are in the position to do) the court will decide the custody aspect in accordance with what's in your daughter's best interest.
THIS COMMENT DOES NOT CONSTITUTE LEGAL ADVICE and are provided for informational purposes only. Answering this question does not create an attorney-client relationship should be taken as legal advice for any individual case or situation. This information is not intended to create, and receipt or viewing of this information does not constitute, an attorney-client relationship. Attorney is licensed to practice law only in the State of New York. All answers are based solely on New York law, unless otherwise specified.
You can check if community legal services can help you. Check with battered or abused women's groups. The only other thing is to find a lawyer who'll take the case and agree to apply for fees from your husband -- but I doubt you'll find anyone.
Custody is determined by the best interests of the child, as determined by a court-appointed expert, paid for by the parties.
DISCLAIMER - THIS IS NOT LEGAL ADVICE, AND DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP. THIS IS POSTED SOLELY FOR GENERAL INFORMATION PURPOSES.