I actually recommend getting a laptop with higher than 1366x768 resolution. That low resolution will limit her ability to multi-task on a laptop especially if she is researching and writing papers at the same time. Dealing with 1366x768 resolution is a real pain; I know from experience.
I would buy the following SONY VAIO SE Series VPCSE1DGX/B for $800 after $100 rebate. It is a 15.5" laptop with a 1920x1080 resolution screen. It has a backlit keyboard and a Core i5-2430m CPU which is more than fast enough for at least the next 4 years based on what your sister is currently doing. It is less than 1" thick and weighs 4.4lbs which is pretty light for a 15.5" laptop.http://www.newegg.com/Product/Product.aspx?Item=N82E16834127691