Given that I am a random person on the internet and my firsthand info is 6 years old, take this with a block of salt. I’m sure someone will post ascensions from recent years to give you a better idea.
Generally speaking QM is not a very competitive branch assignment. The competitive branches tend towards Combat Arms—Infantry and Armor first and foremost. Military Intelligence is as well because there are fewer openings. Cyber is up there as well, because of specific educational requirements. If your DS listed QM as his 1st choice, his chances are good. If he has a high OML, then his chances are excellent.
QM is not a branch that newly minted 2LTs try to avoid, but no one who aspires become a General would choose it. My DS chose a support branch which was not a popular top choice, but he was excited about it and figured that it would be his best chance to get an OCONUS first duty station. He even accepted a BRADSO to get it. If your DS is choosing QM because he is excited about it, he will have an opportunity to differentiate himself from other JO’s who maybe didn’t get their first choice or figured it was the easiest way to fulfill their ADSO.
Wish him the best of luck!