sc
to me this seems awfully quick.
It usually takes me about 3 to 6 months to get to the real part of a boyfriend - girlfriend relationship where you get over the initial excitement and really get to know each other both strengths and weaknesses. This will happen faster if you move in together though.
Essentially after one month, you'd have no idea what your chances of being able to hold it together will be.
If you both have contingency plans should you not be able to stand living together at some point in the future, that you can both afford, and would be prepared to honour even if you (suddenly) thought the other person was horrible, then I think you will be ok. You might never need the plans but you don't want to find out the hard way that it was a mistake and then be broke because of it as well.
I think you are both old enough to make your own decisions about this. It will certainly be good for your social skills.