You can get dowels up to baseball bat blank size. Past 1 1/2 inches, they start to get expensive fast, though, and I don't know if the ones that aren't baseball bats are easy to find in a specific hardwood. Even at 1 1/2 inches, you get birch or maple from woodcraft, though there is a local supplier here that has maple for about $6.00 a dowel at that size.

The last 1 1/2 inch dowel I got from woodcraft was maple, though, and good quality.

I can't remember where I saw the bigger ones, but it wasn't woodcraft.