An important thing to consider before purchasing a machine, is that many of the time-tested brands that once represented quality, have been purchased by holding companies, which exist either to split up and and sell the acquisition as piece meal, or to own managing stock. They have no interest in the quality of the original product and they outsource the product and its parts to be cheaply made so that they can slap the original brand label on a cheap product and turn a profit. In contrast, most manufacturers have engineers that design and develop their machines and parts and they create a list of specs and prints and those specs and prints are are used as guidelines to manufacture machines and parts. In 2006, Husqvarna Viking, Pfaff, and White were purchased by a holding company called Kohlberg. They already owned Singer. White became consolidated with lower end Vikings. The quality Swedish engineering that Husqvarna Viking was once known for, was instead, outsourced to Vietnam and China. I know that my Quilt Designer was one of the last machines that was Swedish engineered using the true Viking prints and specs. I think your Quilt Designer may also have been one of the last. Many people who love vintage machines love them for their quality. I'm not suggesting that it is not possible to buy one of the newer machines and really love it, but I'm just saying be careful with your purchase and research the history of the company and read reviews to see if people are happy with their warranty.
If I were recommending a machine to a new sewist, I would recommend a good quality, used, mechanical machine. A new seamstress can graduate to a computerized machine later. When you buy a used machine, oftentimes feet and accessories can be purchased for a song. Anybody who sews knows that the feet and accessories can cost more than the machine. What a wonderful thing to be able to have a large assortment of feet and experiment with them. Many new sewists who buy a new machine can't afford to get the extras that are made for the machine, and with a used machine they are more affordable. A wide variety of feet will give her more learning opportunities, refine her skills accordingly, and widen her options for creativity. With a mechanical machine, there are less things that can go wrong. How long will the mother-board last on a computerized machine? What is the likelihood that she will be able to find another mother-board if hers fails? I can't tell you how often I have been able to figure out how to fix my mechanical machines myself. On the other hand, in fairness, computerized machines are fun and have many whistles and bells that a mechanical one doesn't have.
Check out PatternReview.com for reviews on sewing machines. There are archives of valuable information available there.
Obviously there are things you know that she would want in a machine. If she likes your Viking, then she probably would like a computerized machine. While I think a used machine would be a good choice, many young people would rather have something brand new.
When you are considering features, I think a machine with the widest possible harp space is important. When I want to clean or oil or repair my machine or change my light bulb, being able to work with something that is easily accessible is important. Being able to change to different needle positions is an important feature. Being able to drop the feed dogs is important. You should make a list of what important features you would like for her to have.
I own a Babylock Mechanical sewing machine, a Janome made computerized Kenmore, a top of the line vintage White/Kenmore, a Viking Quilt Designer, a Babylock serger, and a Viking serger, and a Janome CoverPro CPX1000. I love them all. I don't have any experience with the newer machines, but there are other members here who do and it sounds like they are happy with them and have a lot to say about them.
How thoughtful of you to want to give this little girl such a wonderful gift. You have a very big heart and someone is very lucky to have you in her life. For all you know you could be part of her destiny. Good luck with your choice.