A 12ga works but it can be overkill for doves. A 20ga 2.75" shell 7.5 or 8 shot will work fine. If you're a good shot then you could consider 28ga or even .410. The main problem with those gauges is that you can go through a lot of shells dove hunting, and generally the 28 & .410 cost a bit more than 12 or 20. (unless you reload)

#6 shot might give you a bit more range, but hit a dove with a full pattern and see what you got left.(my friend hit a cock pheasant at 35yds in the center of the pattern with a 20ga choked IC and it was nearly blown to pieces, he left it in the field.)