That's gonna make it tough, I have a little knowledge but it is only for the Verizon model. What I do know is that you are on the latest software version available for your phone without rooting. The rooting of your device I am not sure how to do.
It might not. What I meant more specifically was that I have never rooted any Galaxy S phone, regardless of which carrier it is on. The best I could do is Google how to do it but would be unable to help much as far as the actual rooting or trouble shooting if something goes wrong.
What did you want to root for? Is there a specific reason or did you just want to do it?