It depends. If you have not had fairly regular sex by now (or if you've had none at all), then it could be a very poor decision to ask her away for a "romantic weekend", which suggests continuous intimacy and an emphasis on ongoing sexual activities. It obviously would be pushing sex far too quickly and may well result in the early termination of your relationship.

If you are pretty sexually active already, then ask her how she feels. One month is fairly quick to be taking a relationship to another level, one she might not be comfortable with at this stage. A weekend away sort of implies that you are thinking of some form of commited relationship, and this may be way too soon for her.