I'm the family cruise editor. A cruise to Greece and Turkey sounds great with your child, however I wasn't sure if your child is an experienced traveler. If your child is used to long plane flights, going on tours, etc., then I think it'll be a positive experience. If not, you may want to wait a few years until they are ready for it. (Read the article
I wrote on this site called, "Can your kids do Europe?") Many of the big ports in Europe are a long drive from the main cities (Rome, Florence, etc.) which may be too much for your child to handle. However, many of the Greek islands do have ports accessible to beaches and main towns.
On the other hand, I just returned yesterday from NCL's Norwegian Star in Hawaii and it was a great family cruise. Lots to do on land, ranging from snorkeling, to exploring volcanoes, etc. and the Star is a very family friendly ship.
Let me know what you decide.
Smooth sailing,
Luisa Frey Gaynor