Actually, the true definition of a yearling is a deer in it's second year of life, or between 1 and 2 years old. Fawns are technically deer less than one year old. Call them what you want, but just know that in discussions with biologist, deer managers and anyone who does this for a living, the term yearling refers to the correct definition; an animal between 1 and 2 years old. If you call a fawn (a deer less than one year old) a yearling, you are actually misusing the word, but as long as those you are talking to understand what you mean, go for it.
The problem comes in when people use yearling to describe a fawn, it can be a little confusing to people who know what a yearling is. But, we eventually figure out what you mean after a little while.