I don't have too much advice, but you should look into everything very very carefully - I don't know anything about benefits eligibility, but you don't want to do anything that may jepordise your future in the country. Likewise, you would want to make sure you have a good solid case for ILR should you wish to stay.
(Note: Benefits and access to benefits can be a very emotive, debative subject for many people. My statement is intended to say just make sure, very carefully, you know the law and your eligibility, rather than face value information off the world wide interweb that says do it or don't do)
You can find all the ILR for Domestic Violence on the UKBA website -there are specific requirements for proof (and a husband abandoning you alone doesn't seem to qualify?)
Your daughter is British? You still may be able to apply for leave under a single parent provision as well. (If that still exists)
Do you want to stay in the UK? Does your baby's father want to remain in contact?
This is a highly complicated case and if possible, I suggest you get some legal counsel, rather than through folks off the web who don't really know the ins and outs of all this.
I'm sorry for this situation, I hope you can get all the help you need.