He goes right back to where you found him originally.
I had Dorn in my party so I ran a little experiment. I dismissed him using the "reform party" option in the character screen. There were no dialog options for "wait here", but if it matters I chose a dialog path that was effectively "you're making a mistake"/"it's been known to happen". He then vanished from my current location.
I found him back where he was originally, loitering on the corner outside of the High Hall of the Radiant Heart, in the Temple District of Athkatla.
Here's the exact location on the local area map. Dorn is the blue circle on the left indicated by a red arrow (the other blue circle is a loitering peasant.)
If you talk to him, there is an option to have him rejoin your party:
 I would have you join me again, Dorn Il-Khan.
... Of course he then plays hard to get:
If you go with the third options, he gets annoyed that you've called him a fool, and then agrees to give you one last chance:
I'll give you a chance, <name>. One chance. See that you don't
Is that actually the last chance?
Luckily I had nothing better to do to run a third experiment, and I dismissed him again and went through above dialogs again. Nothing changed, and he warned that he was giving me "one chance" (a second time.) So in this regard it seems like he's like most of the other companions in that you can dismiss and rehire him at will.
(Note that I've not completed his personal quest; I've only done the first stage and murdered the priest; I'm not sure if this has any affect on this, but none of the dialog options appear to mention any his quest line.)