You might want to compare not just needle and yarn sizes but GAUGES as well! While it may sound logical that using needles and yarn half the size suggested in the pattern you can simply double the number of stitches, but how can you be sure? Wouldn't you hate to get close to the end of even the first couple of inches and find out your garment is going to be either too big or too small?
If I were you, I would do a swatch with the smaller needles and yarn and see how it compares to the gauge required in the pattern. Then proceed from there. That little extra time you take may make a BIG difference in your project!
Good Luck and let us know how it works out!