I think you should absolutely buy her some nicer paints! Not sure what your budget is, but this is a nice set. The tubes are pretty tiny, only 5mL but watercolor paint tends to go a long way. They also sell them in 15mL sizes if your budget is bigger. There are lots of other good brands of watercolor paint too.
Some nice quality brushes, paper, or a new palette could go with the paints. In addition, if she doesn't already have them, a nice set of pencils, eraser, maybe a white gel pen, pencil bag are all nice to have.
Better paint and paper over brushes any day! To have paint and paper that behave properly will take a lot of frustration out of learning watercolor. Daniel smith has a beginner set of watercolors on Amazon that will teach you a lot about color mixing. I love arches for paper. The big sheets of hot and cold press are pretty awesome. I do really enjoy my Da Vinci brushes. I don't have the set that you mentioned, I have a squirrel size 2, and sable travel brushes for sizes 10, 6, and 4 - love them! But I use them just as much as a cheap water brush and $1 brushes from michaels.
Oooh this is a fun game:
sorry for stupid long links