This sounds a lot like what I went through in my early 20's (minus her having the kid already-which is a major game changer). GF was from a troubled home and lived here in CO. with her mom and step-dad. She was desperate to get out of her current situation. She wanted to move to Memphis to be closer to her dad and other family. I was a Colorado boy from birth with the steady family close-by.
So, we actually went and visited her family in the Memphis area first. I found out that despite the glowing reports she had told me, her dad was a drunk. He was a huge a-hole. She of course fell in love with the idea of being back "home" again and wanted to move. I dug in my feet knowing I didn't want any part of that Memphis, Tenn./W. Memphis, Arkansas area. I certainly didn't want to be around her family who looked like the poster children for the typical "redneck Arkansas family". I just began stalling and pointing out the things that weren't quite right with the plan to move back there.
I would suggest taking a trip there if possible to meet her family, check out the area, etc.
How did my story turn out? Well, we stayed in Colorado and I went to school. We got married. Moved to Wyoming and bought a house. Had 3 great kids. Moved back to Colorado and eventually landed a good job at a University while my wife is currently in school (put that off having the kids). So, I guess what I'm saying is she may be right for you, but perhaps where she wants to move isn't the best idea. Move (or stay) where it makes sense. I was promised jobs by her dad, too. Of course, if he had such great leads, why was he working odd jobs to support himself?
The big differences in our stories though is my wife has usually been employed (even though she had some real crappy jobs) and she didn't have a kid when we got together.
Visit the area first, but be prepared for her drive to move there to be even stronger. Which means if it doesn't feel right, your drive to NOT move there has to be that much more strong.