We potted the cutting in a container. The cutting took root and flourished.
Unfortunately, the branch points of our new Plumeria are low and as the tree grows it takes a lot of area (see the picture in the upper right).
I decided to divide the tree into three parts, by cutting the two side branches and transplanting the cuttings into new containers.
I cut the branches at an angle so to provide as much surface area as possible for roots to form.
I then dipped the cuttings into rooting hormone (see picture to the right).
The most important thing about rooting a Plumeria cutting is to not overwater. I use a soil-less potting mix of three parts Fir Bark, 1 part Perlite, and 1 part Peat Moss (see this blog entry). This potting mix drains well.
The picture below shows the the Plumeria plants. The one in the center is the original plant.
For an update six months later, see this blog entry.