My son, now 13, had a very pronounced underbite. We were told he would need the "jaw breaking surgery" when he got to his early 20's and was fully grown. We were given the option of trying braces early to try to manipulate his jaw and bite while he was growing. He got braces at age 10 and wore them until he was 12. Before the braces were put on, he actually had to have a few baby teeth removed since they weren't coming out on their own and he had to have a gum surgery because the stress of having so much pressure constantly on his bottom jaw/bite caused his gumline to wear away in front of his bottom front teeth. Our dental coverage paid for the extractions and gum surgery, but not the braces.
The braces solved the underbite and almost 2 years later (he's almost 14)the bite is still as it should be. His orthodontist is so pleased, he is now using my son's case as a teaching tool because his underbite was so severe (he had a little bull dog bite). There is always a chance the jaw could shift back, but his orthodontist and dentist don't see any evidence of it now. We are very hopeful that he won't have to deal with this again. Keep in mind, the braces were for the jaw problem, not for cosmetic improvement, so while my son's teeth were pretty straight as a bonus, they may shift over time.
Lastly, I just want to say that his dentist never suggested doing this at such a young age as your child. We always knew the problem existed, but he waited for his permanent teeth to come in so we could go from there. You may want to consider a second opinion.