Apple seems to offer every size now - all using the same eco system of same apps on iOS6. The iPad mini has all the pixels of the iPad2 1024 x 768, but on a smaller 7.9" screen. So the resolution is still pretty good and better than most laptops. The iPod Touch has super fine retina resolution 1136 x 640. The iPad mini weights 0.68 lbs (308 grams), the iPod Touch retina weighs only 3.10 oz (88 grams). So the trade off is screen size, weight and price.
Screen size: For email, txt, Facebook, Facetime, reading books, iPod Touch can do. For watching movies, playing games, the iPad mini's larger screen has an advantage. I like reading iBooks on my iPad vs my iPhone5, since the screen is bigger.
Weight: mini (308 grams) vs iPod Touch (88 grams) - no contest, Touch is almost 1/4 the weight.
Price: Touch starts at $299, mini $329. But mini offers cellular 4G (which means a monthly data plan of at least $10/mo on the share data plans). Chances are you will give your daughter a cell phone soon, so perhaps mini cellular is not a consideration. After all, with Hotspot, you can turn the phone into a WiFi hot spot to give data access to either device.
So figure out the size vs weight, ask your daughter about applications and about carrying something all day.
For some technical background on the screen resolution, the iPad mini display is pretty sharp - has 162 pixels per inch (ppi). The iPod Touch retina display has a very high resolution of 326 ppi. (MacBook Pro 15.4" display regular 1440 x 900 has 110 ppi, retina display 2880 x 1800 is 220 ppi)
Good luck.