Doesn't sound too much of a problem to me. Girls are more mature than boys at that age so you are probably on the same level....presuming the 13yo is a girl...
age gaps... often there are concerns, people worry, whether going out with someone, 3, 5, or 8 years older than you is ok. If your not breaking the law, both mature enough and want to make it work, then go for it! If other people are unhappy then they're just either jealous, or arent living in the 21st century. good luck.x