My 1-year-old female cat hasn't gone into heat. Is that normal?

Hi and thanks again for your question.
I think in this case there are basically two possibilities: either she did not go into heat (that can happen anytime up to the 18th month or she went and she showed few signs.
It is not common to observe vaginal bleeding from a cat in heat. The most notable signs of estrus in cats are behavioral. Most cats become very affectionate, even demanding; they persistently rub against their owners (or objects such as furniture), constantly wanting attention. They roll on the floor. When stroked along the back or spine, they raise their rear quarters into the air and tread with the back legs. They also become very vocal. These behavior changes often become annoying to owners, and sometimes owners think their cat has some unusual illness.