Do I need a second plum tree to
get fruit?

Yes you do. Plums require cross pollination by bees from a different variety of plum. Here are some tips on selecting a second tree to plant.

Related Videos:
Pruning Nectarines, Peaches, and Plums
Fruit and Nut Pollination

Related Resources:
Home Garden Plums
How to Grow Plums in Your Home Garden