The person getting you the buddy ticket will tell you if it works for minors. However, as has been stated before, because you are flying on standby, then there is a chance you may not get to where you want to go when you want to go there.
Depending on how old you are, some airlines may need special instructions from your guardian/parents regarding you flying by yourself. For example, if you are 14/15, you might be ok. My 14 year old has flown on his own. If you are 11/12, they may not let you on the plane by yourself unless some prior arrangement has been made regarding who is greeting you on the other side, and other such red tape. You want to be clear about these things before buying any tickets. As you are a senior, and may not have this, you will need some government picture ID to get onto the airplane.
Obviously, this is not advice that is a substitute for discussing this situation with your parents, but hopefully it helps you get started. good luck.