The doctor is the one who will tell you at what age it can be done. We don't know the answer to this.
You should not feel like you have to justify getting your child's face to look normal again. If she had busted a tooth, would you just let her walk around with a hole in her smile? No.
You don't have to wait until she's older to understand and want to do this. Children have surgeries they don't understand all the time. Tonsillectomies, ear tubes, tongue-tied snips, etc. There is NO difference. You do what needs to be done, and don't get hung up on the issue of "cosmetic". Your daughter is NOT an adult. It shouldn't be up to her to express concern about this "shadow" on her face. It's your job to take this in hand and fix this for her.
Get the ped to give you a referral to the specialist and work with him or her to decide on a plan. To be honest, if it were me, I would want to get that surgery done now so your daughter doesn't remember it. AND so that she doesn't remember having that "black eye" all the time. (Though it may be too late for that.)
Consult with the doctors on this. Try to let go of this cosmetic hangup.