In vitro paternity tests are dangerous and only done in cases of serious medical issues. But after the kid is born, it is much easier.
Just so you know all your rights, assuming you are in the US or a similar western country, you have the right to sue her to force her to take the paternity test. Of course, if it is your kid and you get the court involved, you will end up paying court-ordered child support. It's up to you. There are a few strategic advantages by being the first one to file court papers, one of which is choice of venue. If she moves away, then sues you for support, you'll have to go to court wherever it is she moved away to. Cases can be won that way, just by making it too expensive and difficult for the other side to show up.
Another thing about your right to see the kid and your legal duty to pay support, they are two separate things. If you do get stuck with support, don't just assume you get visitation rights, too. You may still have to sue to get those, but if you are paying support, then you should win visitation.