I agree with gilnikche and feel that before things get worse and winter isolates your friend further, you should help her to get some help. She is possibly so low that she has no desire to do this for herself. You may have to be pushy and you may have to inconvenience yourself for a while in getting together with her, but it would be a wonderful gift to give your friend and her baby. BTW, the things you mentioned offering like watching the baby while she gets a bath are totally on the right track. Out of trying to be polite or strong she may turn you down if you ask, so depending on how it sounds given your relationship, you might skip asking and try just announcing it as a done deal, e.g. "You have been working so hard and deserve a break. I will be over at 3 this afternoon to draw a warm bath for you and then watch your baby while you relax in the tub." Or whatever you think she would like. Taking some leftovers or even a healthy frozen pizza for her to eat would also be great.
You are such a great friend to recognize her struggles and post here and want to get her some help. She is lucky to have you in this time of need.