All jokes aside. Leases are a business instrument. We hear it everyday not to mix business with pleasure.
If someone is in a relationship and the other person wants to move in they should already know they are contributing to the household. If they don't then that person isn't the one for you.
If you're in a new relationship there really isn't a reason why that person should be moving in so soon but that's more subjective. No one on this thread knows exactly why you would want her to move in so soon so we can't really give a good answer to your question and we shouldn't be the ones helping you answer that to begin with.
Now to the question. If she decided to quit paying or a situation came up (loss of job, etc) where she could no longer pay, would you enforce the lease? She's your girlfriend going through a tough time. Could you really kick her out for that. You want her to be your tenant but you are emotionally involved with this person. Your judgement as a businessman is weakened.
A lot of people are saying that if you guys break up then she will want to leave just as much as you would want her to leave. Who's to say that is true? You've only been with her 6 months. She could be some nut job and decide to dig in for the long haul. You could deal with this by having her on a month to month agreement but you would still have to wait 30 to 60 days. Let's say over those 30 to 60 you decide to get back together. It's all good for a little while then you're breaking up again. This is getting messy. Now that lease is becoming pointless and worthless.
If she signs a lease you are asking for more trouble than it's worth. I'm looking at some of the worst case scenarios but all I know this could be great for you and you guys could live happily ever after BUT it could also be one of your biggest mistakes.
There are some many more cons that I haven't mentioned and so few pros to this.
Good luck @Adam Pierce