The Nabi Jr. can be rooted easily following the guidelines below. I rooted mine in under 15 minutes. Of course, rooting voids your warranty and I am not responsible for anything that might go wrong.
The first step is to install the ADB drivers. I found this video guide which made the process easy enough:
Then I followed the instructions for rooting with Root_with_Restore_by_Bin4ry_v18 at this link
I chose Normal - Option 1.