Your State of Jailbreak:
There is a jailbreak available for your iPod touch however it is tethered which means you will need to rerun it every time you boot your device. If you update to iOS 5.1.1 there is a fully untethered jailbreak available.
redsn0w is a very solid jailbreak that takes just a few minutes to complete and still is about as robust and full featured of a jailbreaking program that you can get. Using redsn0w 0.9.10b6 you get a tethered jailbreak with options including custom bundles and multitasking gestures.