I don't recommend it if there is any way you can wait until you get back to your own computer. If you do decide to go ahead, the process is going to be pretty much the same as moving to a new computer. And you are going to have to do it twice. Once to set up on you sister's computer, and again when you get back to your own.
First, the smartest thing you can do is set up you own user account on her computer, with your own log in. This will keep your from messing with her iTunes library. I will also be easier to remove all your stuff from her computer when you are done.
When you've done that and logged on as you, open iTunes, go to the preferences, Devices, and turn off auto-sync. It's a checkbox under the device list (which should be empty).
Make sure you are using the most recent version of iTunes. It should be version 10.2.1. You can check in under the File menu, About.
Now hook up your iPad. It will probably say something about erasing your stuff (say no) and Transferring you Purchases. You are going to want to do the second, just incase something goes wrong and you need to recover.
So, go to the Files menu and choose Transfer Purchases From. . . This can take quite a while, depending on what you've got on the iPad. If you're looking at a nearly maxed out 32 GB iPad, we are talking hours.
When you've done that, find your device in the list window to the left and right click on it. Do a Backup. Again, depending on what is on your iPad, this can take some major time.
To be safe, also go into the Store menu and Authorize the computer. You'll need to be signed into your account in iTunes. Be sure to remember to go back here and Deauthorize the computer before you remove your stuff from the computer and go home. It uses up on of the 5 averrable authorization slots. You can recover it later if your forget, but it's a pain.
When that is finished, you can finally allow the iPad to sync with and be associated with the iTunes library. All this was necessary, so that if something goes wrong you'll be able to recover your iPad.
Now, with the iPad plugged in go to the summary tab and check of updates. When it says an update is available choose to just download it. This frees up you iPad for use in the mean time, and prevents the update from happening until you are ready.
When the download is done you are ready to update the iPad.
Make sure the iPad has a reasonable charge.
Make sure all connections are secure.
Make sure the computer is plugged into power, and not likely to shut down in the middle of things.
Start the upgrade. For not reason short of total failure and multiple reboots of the iPad should you disconnect it before it is finished. It should only take about 15 minutes, but I would not interrupt it unless it's been more than an hour without finishing.
When your iPad is nicely updated, you can remove the account and your iTunes library on your sister's computer, or leave it until later. Just remember to go back in and deathorize the computer before you remove it.
When you go home to your computer you are going to have to go through everything but the update and authorization process again.Make sure you've updated iTunes to the current version there too.
Each time you do this the iPad associates with the new computer. It will not remember the old computer. It wasn't designed to sync with more than one computer and iTunes library at a time.
Disclaimer: This procedure should work, to the best of my knowledge. My knowledge is not infinite. You'll probably run into details that you have to figure out for yourself. I don't have the resources to duplicate the proceedure, so I am unable to actually do a step by step set of instructions. I'm working from memory and how things are supposed to work. If you can find a more reputable source of procedures (and almost anything online would be more reputable) use them.
Also, if you do this and it works or not, let me know and the what happened and anything you think would help the next person. That way I can at least not give bad advice twice, or hopefully improve on good advice.
