you can be 2 months or older. I dyed my hair when I was 2 years old ( I put some pink in it. at first my mom didn't want me to) When doing someones hair who is younger then 1 you actually can't use anything strong such as bleach, It's best to wait till their hair is stronger. So I would tell you at least 2+
I think there is no set age for one to dye their hair. However, if you are young, you need to get consent from your parents. You should also wait until you are mature enough to decide on a specific color for your hair. Before dying, consult your hairstylist for the right dye product and color.
I agree with the last person who answered. There are no age limit that I know of but if you are young you do have to ask permission and some schools do not allow certain colors so be mindful of that. If you are not young than go ahead but not all colors go with everyone so choose wisely.