How to get iOS 4.3 on the iPhone 3gs?

If I can't how can I jailbreak my phone.

Added (1). FREE suggestions please.

You can't

Upgrade to 5.1.1 and jailbreak it from there. Here is a video on how to jailbreak 5.1.1:

If you want to wait a few more days, you will be able to update fully to iOS 6.1 and be able to jailbreak it as well. More info on that here:

Hope this helps!