Here is a quick tutorial with the details for jailbreaking your iPad 2 running iOS 5.0.1. This exploit from pod2g has resulted in an untethered jailbreak via redsn0w 0.9.11b1 from the iPhone Dev team. There are a few parts that I fast-forwarded the video while the iPad 2 was loading, etc. The hardest part of the process is probably getting your iPad into DFU mode, but this becomes quite easy after you get the hang of it.
This tutorial is pretty simple, please drop a comment below if there was anything I missed. After you spend 10 minutes jailbreaking your iPad 2, you are ready to enjoy Cydia on your iPad 2 along with your hassle-free untethered jailbreak. Be sure to install Springtomizer 2 on your iPad along with Activator for your initial jailbreak tweaks.