Andy,
Yes, the bigger the machine the better for resawing, but it can still be done on smaller machines -- with limitations (power, resaw height, blade tension).
Power can be dealt with by a sharp blade and a slow feed rate. Smaller machines usually have less stout frames so they can't be tensioned up for optimum blade performance. (Years ago I had a 12" band saw once that you could actually measure flex the frame if you over tightened).
A 12" should hand a 1/2" blade. Be sure its designed for resawing, something like Woodslicer or Timberwolf.
Tension it up as tight as you can, get your fence and drift dialed and and give 'er a rip....