But you are using the same computer and iTunes library, yes?
I you want to keep your stuff separate you'll need to have separate iTunes libraries. You can do this on the same computer. The easiest way is to have two user sign ins for the computer, and sign in to your own user before syncing the iPad.
Getting all your stuff into the new library, and removing it from your daughter's (or vise-versa) is going to be a bear.
In the first case you can try the instructions I'll leave below to start one of the accounts syncing with the new library (instead of new computer).
The only way to get the stuff out of the old library is to delete it manually. Don't do that until you are sure the new one is working properly.
Here is Apple's recommendations on how to transfer all your stuff to a new iPhone. With a few modifications it works very well for moving your iPad to a new computer. Wish I could find one as well written for the actual task.
iOS: How to back up your data and set up as a new device
Start by going into iTunes Preferences (before connecting the iPad) and turning off auto-sync. It is under the Devices tab. This will prevent any unwanted syncing before you are ready.
Do only the parts that apply to your information/situation (i.e.; if you are syncing contacts with Google, don't do the Personal Information Manager part. Stop when you get to the Restore step.
It would be wise, after the Transfer Purchases option to go through iTunes and make sure everything (media, app, book) got transferred. If not you may have a few more steps to insure all your stuff gets safely backed up on the computer.
NOTE: If you have picture albums in the Photos app, and they are not backed up somewhere other than the iPad, you need to save them first before doing anything else. The first sync will remove them. The PhotoSync app works well for this, and you can use it before starting any of the other procedures.
The quality of the pictures recovered this way will probably not match the originals. iTunes optimizes photos for viewing on the iPad when it syncs them.