IMO that child has a lot of growing to do, and the thing may also self-correct.
If he/she were my child, I would wait a few years while doing continuous ongoing research on my own to give it a chance to self-correct.
It is ridiculous IMHO to make irrevocable surgical changes with a knife to a child so young and mutable- Sounds like the surgeon is < w i n k > having a slow week to me.
BTW, in my Mother's Chihuahuas droopy ears indicate a nutrient deficiency. When it's resolved they stand up straight.
I'd get the child checked out enough medically to know there is no tumor/bloodclot or something like that causing it. Then take the child to a Cranio-Sacral practitioner or a very knowledgeable pediatric Osteopath (One who can determine whether this is resulting from a forceps/birth injury causing misalignment in the cranial bones- sometimes those take a few years to show up) or even to a well-researched pediatric Chiropractor before I'd ever let surgery happen to my child for a thing like this..
Actually, if you can find the most long-experienced midwife in your area, she may be able to help you the most with advice and/or references for practitioners.