You certainly will enjoy new ports of call if you go on the Diamond Princess. I think that what you have to decide is whether you want a bigger ship experience or a smaller ship experience. There will be more to do on the bigger ship, but you will have to share spaces with more people.
Also, if you are in a mini-suite, the minis on the Dawn are much nicer than the minis on the Diamond. Then there is also the issue of balconies - most of those for minis on the Diamond are uncovered. The other balconies on the Dawn are generally more private than those on the Diamond.
Since the Diamond is a larger ship there probably will be more kids on that ship.
I would check with Princess to see how many children they generally get in March on the Dawn to see if there would be enough to interact with your daughter. You might also want to check out the children's program on each ship to see if one offers more than the other.
All of that said, we were on the Sea Princess Southern Caribbean last March and had a lovely time in Grenada and Dominica. The people on both islands were very friendly and welcoming.
That's my 2 cents worth.