yes you can "pick up and knit around the bottom" but you can't do it from the ribbing so you will need to get rid of that first. Pull a thread in a row above the ribbing and pull it out or unpick it. (you can't unravel bottom up on ribbing but you can with stocking stitch.) You can then pick up the stitches and knit down. the sts will be Half a stitch off but that won't matter.
I'd go for a blanket as well. I Love doing blankets. You don't have to worry quite much about size and gauge (unlike a garment) and they are always useful or appreciated as gifts. You could put 2 or more strands together as 'whistlepig' suggested, to do it bulkier and quicker, if necessary. there are loads of blanket pattens about. here's some others. http://www.knittingpatterncentral.com/directory/afghans.php