What a difficult situation you find yourself in.
What everyone has said already, please ask others for help. They will feel awful if you sit there without help and they didn't know about it, that's what friend and family are for, plus you will not need to depend on them forever, but you may well need practical helps with things like looking after the dog or even somewhere to live. I may be reading between the lines, but I also get the impression you don't want to tell them what has happened, perhaps worried about their reactions, again, don't worry, you are not the first person to be in this situation and they will care about you.
As for benefits, if you think you are going to be made homeless, ring your local housing office and tell them what your situation is, and that the rent/utilities are about to stop, and get some advice on what you will need to do if this happens.
Also try CAB or ringing the benefits advice line for more information, you are definitely entitled to more than just ESA once the baby is born, and being pregnant may entitle you to more anyway:
www.direct.gov.uk/en/Diol1/DoItOnline/DoItOnlineByCategory/DG_172666
Have you thought about moving back nearer friends or family? If nothing is keeping you in this area, have a think about what would be a good place for you to be based, given that you will be on your own.
You need to talk with someone, like a friend, who can help you see the options, perhaps having a dog and a car and all these expenses is a bit impractical, will you need the car in the future? I think different solutions will present themselves once you start talking to people, either professionals to help you with benefits, or your friends/family.