It depends on the couple, of course. If your religion or personal bias say DON'T live together, then you shouldn't. Research shows that people who live together are actually LESS likely to marry than those who don't. However, I think moving makes sense for two reasons:
1. The cost of living is a heck of a lot lower for two people living together than the same two living apart. Since money is the most common reason for divorce, I suggest you maximize your assets, and lessen stress on the relationship, in any way you can.
2. About half of all marriages fail, and divorce is more complicated than a breakup. So, if it feels right, take the relationship on a test drive. See how it holds up.