Congratulations on getting an egg from her so young. Some breeds start laying earlier than others and it's not unheard of for some to start as early as 16 weeks, but usually it is about 20-25 weeks. I think time of year may play a part too. Springtime should have a beneficial effect in that respect.
I don't know how much experience of chickens you have but she doesn't have to be mated to lay eggs. There are a lot of people who don't keep cockerels who still get eggs.... in fact... pretty much all the commercially produced eggs in the world are from chickens that have not been mated or even seen a cockerel. A cockerel is only required to make the egg fertile. A hen produces and lays an egg as a natural part of her reproductive cycle. If she hasn't been mated then the egg has no chance of developing into a chick. If she has been mated then the egg will be fertile but will then need incubating to develop into a chick. The egg is produced and laid irrespective of her being mated. Hope that makes sense.
I know that, I have roosters and many hens, usually if you have hen who are fertile and suppose to lay eggs, rooster will stick around them to mate and fertilise eggs just before 10 days of laying, that I didn't noticed in this case.