Does the pattern give a guage? I mean, does it say you should get 7 stitches to the inch or something similar?
If not, what needle size does it say to use and how many stitches do you cast on?
Oh, and can you post a link to the pattern or even just a picture of it? If we can see the general shape of the hat, along with the needle size and stitches to cast on we have a better chance at helping you with a yarn substitute.