You might not want to use larger needles, the stuffing could poke through. That would probably make it larger around and not that much longer though. Simplest would be to knit the body longer between the tail and where you put the arms on, or dec for the neck and possibly knit the head a little longer. It would be skinnier that way so you might have to add more stitches. That shouldn't be too difficult even for the 'butt' part which is like turning a heel on a sock, it's just a larger heel.
A combination of all your suggestions might just work. I'll try a heavier yarn with a larger needle and add a few more stitches as well. Can't wait to see what happens. Thanks so much for your ideas and support!