Spire, usually the top of the steerer is cut to the exact length, so you'll have nowhere to go if you raise the stem. If for some reason yours isn't, then usually there will be spacers between the top of the stem clamp and the cap, and you can just move them under the stem. But that would be unusual. Most likely, your steerer is cut and you have no space above the stem clamp to reaise it.
Here are the options:
1) Flip your stem, if it's not already. If yours is not a stem that extends at a 90-degree angle from the steerer, then turning it over will give you more rise. Typically, many road bikes come with stems that are parallel to the ground in the "down" position, and give quite a bit of rise in the "up" position.
2) Buy a new stem with even more rise. (Or an adjustable stem, as previously suggested, but that will cost more and be heavier.)
3) Buy a riser (a tube that clamps to the top of the existing steerer and adds a couple of inches to its length). These are $20 or so, and I wouldn't have one on my bike if you paid me. But maybe that's just me.
4) Replace the fork, and this time have the steerer cut longer.
5) Replace the bike, and get a better fitting done on the new one.
As to your question about diameter, it's either 1" or 1-1/8". Current 1000's are the latter. You can measure it with a caliper.
Training: 2002 Fuji Roubaix Pro (105 triple)
Commuting/Daytripping: 2001 Airborne Carpe Diem (Ultegra/XTR, touring wheels)
Commuting/Touring: 2000 Novara Randonee (Sora/Tiagra/LX, fenders, lights)