I see how you used your method. Looks fine to me.

Just to add a different perspective, here is what I did.

I assumed no restrictions and distributed the 5 dolls among the 5 kids (5 ways for the first, 4 ways for the second, 3 ways for the third,......1 way for the 5th)

This gives you 5!, which is 120. However, since two dolls are identical, you have to recognize that this method will count the possibilities where the two girls with the beach dolls would essentially swap the same doll, which would not produce a unique arrangement. Therefore, you divide 120 by 2 and get 60

Now, take out the restriction, which means finding the number of arrangements where the youngest niece would end up with the G doll, and then subtracting that number.

G doll would be distributed only 1 way (youngest niece), the remaining dolls can be distributed in 4,3,2, and 1 ways respectively. So 4! x 1 = 24. Again, however, you need to divide by 2 to eliminate the additional arrangements caused by the two beach dolls. 24/2 = 12

60 - 12 = 48 possible combinations