Provided she doesn't play high spec games which take a lot of resources (gamers' games) then any of the laptops you can buy from Tescos, Woolworths and so on will do the job and will probably have a dvd drive as well.
You need to discuss with her physical size - a big screen is nice and essential for graphic designers but makes the laptop bulky and heavy for carrying around.
Have a good look at the online stores where you can easily compare the specs. I suggest you look at Tesco, Woolworths, PCWorld, Argos.