unknowndomain said "technically"
But you can if you wish. All you need to do is authorise your sisters ipod to your itunes store account.
Or alternatively to quicken things up. Sign into ur itunes account on the ipod touch, and download the apps you know you have purchased. You will get a message when you tap on the install button
"you have already purchased this app, would you like to download again for FREE"
Simply download all the apps you have on your iphone to her ipod touch.