For earrings, the quality of the diamond does not need to be quite as high as it would be for a more visible piece of jewelry. Does she have long hair? Will they be completely exposed? How much of the diamond will be covered by the setting?
If I were choosing a pair of earrings, I would look in the SI1-SI2 range and for a color in the range of H-I. The cut can be good - very good. Perfection isn’t necessary in this case
Good luck!
I would worry about the color or clarity. I would mostly look at the cut and carat.
For studs - if they arent enormous — you could probably very go down to a I1 as long as the inclusions are WHITE and the cut is a Very Good or Ideal. Color can probably also go to an I again if the cut is very good or ideal.
Order online and save money - if you do make sure they have a good return policy in case they arent what you expected.