Call CPS, without a doubt. That is the one thing I know for sure, everything else is based on my experience and may not work for her based on her location or other factors. I'm in Colorado.
1) You can call your local police department to schedule a time to be present while you are moving out. They told me they could stay for one hour, and I did not have to file a police report. I was scared, like your friend, but I would try again to encourage her to file a report.
2) In my area, there is a domestic violence support center called TESSA that provides resources like housing and counseling. They also have volunteers that will go to appointments or court hearings with you so you aren't alone. They're also there to look out for you if you decide to go back to your abuser, which happens all too often.. Look into a similar program that is near you.
3) It was fairly easy for me to schedule a hearing at the courthouse and get a temporary restraining order for me and my daughter. They honestly don't do very much against abusers, but it's a scare tactic that works for some, and at the very least it can provide some comfort. Remind her she's not taking the baby away from their father by seeking help. There are still be ways for them to have a relationship while making safety the first priority, which leads to
4) File for full custody, and ask the judge for supervised visits with the baby only, and preferably through an established agency if that's available, and not family or friends. Both steps 3 and 4 are easier if at least one police report has been made.
I was lucky enough to have my family's full support, which included a home to go to when I left, so I don't know much else about housing situations for her, but I know there are shelters all over the place. It's not ideal, but it's safe. Also, my abuser escalated at first and it was extremely difficult, but eventually he disappeared and I haven't seen or hear from him since. I've found this to be the case with other victims I've come to know, but it's not the same for everyone.
You can offer all of this support, and definitely intervene with CPS, but after that there isn't much else you can do but tell her that you'll be there for her now and when she's ready to leave. In the end, it has to be her decision.