the bigger the better!
A woman that I purchased diamond earrings for was extremely happy with the 1 carat total weight, princess cut. Although you should also take her height into consideration, and determine whether or not the size is too large or small. 1/3 is a good size too however, I am sure she would appreciate the gift.
Just keep in mind when buying a pair of earrings, if it says one carat for example, that means each earring is only 1/2 a carat. The total of the pair (both earrings together) is one carat. A lot of people don’t realize this when buying diamond stud earrings.
Minimum of 1 carat for each ear.
That is a bit small. You have to see what the total diamond weight is. If the TDW is 1/3 carat, each stud is 1/6 of a carat. If the TDW is 1/2 carat, each stud is 1/4 carat. You’d probably want each stud to be between 1/4-1/2 carat so you should look for 1/2-1 carat in total diamond weight.
If you go too large and get say 2 carat TDW (1 carat each stud), you are going to pay a lot, they will be heavy on her ears, and the bigger they are the faker they may seem. (Many times larger diamonds (2+ carats) on the average Jane may be mistaken as CZ rather than the real thing)