You will need your own AppleID, but just get a free email address (gmail, hotmail, MS Live, aol, ...) and create a new AppleID for yourself.
Then, delete the iCloud account on your iPad, and log in with your new AppleID to create your own iCloud account. You can also create your own iMessage account with the new AppleID if you do not want to share messaging accounts.
Keep using the original AppleID for the iTunes and App store purchased content so you both can share that.
P.S. if the iOS 7 update is complaining about lack of space, that has nothing at all to do with iCloud. That means your device does not have enough space and you need to delete things on there to free up storage. You can also update via iTunes on your computer, which will require less space available on the iPad itself (since the iOS updater gets downloaded to your computer and run from there).