Having seen the movie recently, I completely agree: by that point, Dredd is low on ammunition and would have no compunctions about taking ammo from the outlaw Judge he killed. It also would not have taken long for him to do so, so he was not forced to leave it behind due to time constraints.
The only reasonable explanation I can think of is that he was unable to do so. Perhaps the Judge he killed first had no spare ammunition? If he had been on a busy patrol before being called in (or had been using rounds enforcing other illegal activities) he may have been low on ammunition, having only the clip in his magazine. It would seem pretty sloppy, but he is a corrupt Judge - he likely doesn't stick to the Book the way Dredd does. He also wouldn't see a need to have full ammo before confronting Dredd - he expected to kill Dredd without problem, ambush-style. A few rounds to the head and the job's done.
Thus, it's possible that he only had the rounds in his weapon. Getting the magazine clear of his Lawgiver might be a process that only he could do (or someone at the armory, with an override code). He also may have carried his additional ammunition in a pouch or pocket sealed by a similar lock that only he could open.
We can't be sure which it is, but the only reasonable excuse for Dredd not having his ammunition after executing the outlaw Judge is if there was no retrievable ammunition.