Ya, should be able to go through your camp. I didn't do it during my army days; my wisdom teeth refused to come out.
So for my case it was only extracted recently. I got a referral letter from Polyclinic to NDC. Surprisingly my appointment was pretty fast; just about a week. And lucky for me, everything covered by Medisave (yes, still my money). So better to do it while you are still serving your NS.