That can work, size 9 needles and a DK yarn (22sts/4inches or 10cm). For my tension it would be rather light and lacey but your tension is probably tighter than mine. Usually, that weight yarn is knit on 3.75-4.5mm needles (US5-7) but you may not want that density of knitting.
Do a square with 32sts and see if you like the feel of the knit fabric. Then you can adjust the needle size until you get to a knit square that you like.