Yes, if your yarn is thinner and you knit with the larger needles, you'll probably get the same gauge, but the sts will be looser and more open. For some things this may not matter, like a scarf or shawl, but you might want a little denser knit for a sweater or hat. So use smaller needles, 8 or 9 mm and see if you like that fabric. Then take your sts per inch and divide it into a larger size of the pattern (to get more stitches) and see if that will give you the finished measurement you need. What pattern are you making? If it's online, a link to it will help us to look at it and give you more specific advice.
sue- knitting heretic