Yes, it is normal for an intact female - she is coming into heat. As already mentioned, you need to keep her well away from your male if he is also intact, for at least 3 weeks. A pregnancy at this stage would be rather like a 10 or 11 year old kid becomming pregnant (and if it were to occur, the best thing for her would be a spay/abortion).
Once her heat is finished, you may find that she has a false pregnancy. You also need to keep a close eye on her for signs of pyometra, which is a potentially fatal infection of the uterus and a risk with every heat cycle.