If it's only 10.5' no you dont need a damper. Get a probe thermometer and control the temp with the draft know on the doorI apologize, entirely my fault as I'm not up to speed on all the terminology.
10 1/2' from stove collar to flue gas exit at cap. 23" from flue collar to flue gas exit. I didn't know why the flue collar measurement mattered ( that's where my mind went when I read collar) but there's a lot I don't know. Sorry