Mark - Fruitwood of any type (plum, pear, cherry, apple, etc..) makes excellent turning wood. As to when to turn it, that depends. Many of us turn things for dead-green wood, but you then have to carefully dry it to avoid cracking. There's lots of methods for that, including putting it in a paper bag with wet shavings from the turning session and allowing the moisture to slowly diffuse out of the bag. Other methods include replacing the water by soaking the turning in PEG solution, and/or using a paint-on sealer like Anchor Seal.
If you want the wood to dry somewhat before turning it, you will need to split the log at least once down the middle (i.e., with the grain). If you don't do that, the log will split on its own as it dries, and perhaps not in ways that are desirable.
