The lady should certainly get legal advice immediately, there may be other issues to be considered as well as immigration status, ie custody/access to the child, securing an injunction to prevent violence, division of any assets.... it's a messy business.
There are special provisions to get ILR without completing two years' marriage, but there has to be solid evidence of the violence, eg from the Police; but as far as I know, there is no provision for public support until the ILR is granted. Women's refuges will do their best to help, but are desperately under-resourced; nevertheless, they may have access to charitable support for organisations like the Red Cross.
Every effort should be made to expedite the ILR application - she should try to get hold of as much documentation (and cash!) as possible when leaving the house, she should obtain proper and specialised legal advice and other support first, and she should approach the local authority to see what their attitude is about how they would fulfil their legal duty to support the child - would this extend to supporting the mother as well? (Note that the child has to be supported not because they are British, but because they are a child).
Check this page for valuable information and links:
http://www.womensaid.org.uk/domestic-vi ... 0100350002
Remember that until ILR is granted, the conditions of the spouse visa continue: she is allowed to work. So if someone can help with looking after the child, or if she is prepared to leave the child with the father, this would solve the problem of public funds.
In my opinion, it is essential that someone in such a situation leave ASAP, as the longer they stay the more difficult it may be to escape; on the other hand, it can only be when she is ready, she will need to consider possible wider consequences of a split, perhaps in the home country where there may be little protection for vulnerable family members.
The Refused are coming day-by-day nearer to freedom.