polka-dot wasp moth - obviously a female. Sure is pretty, huh?!

Congratulations, you have an Oleander Moth. Also called a Wasp Moth for the way it looks.

Wiki information about it.

Thanks for the quick response! Yes, it is really pretty and I am sure glad it's harmless as I had my hands within a couple inches of it as I was twisting around leaves trying to get the perfect shot! She layed far too many eggs for my one small desert rose and there aren't any oleanders growing in my neighborhood. Will the plant come back if I let the cats eat all of the leaves?

Neighbor's desert rose was defoliated by one. It was hard on the plant, it took a while but it did come back. Am i remembering correctly that some people have a sensitivity to contact with the spines of these caterpillars?

From Unv. of Fl regarding affect on oleander:
(which I think would apply to adenium as well)

"Total defoliation will not kill the plant but, if it occurs repeatedly year after year, the plant may be more susceptible to other pests such as scale insects."

Here is a link that might be useful: Oleander Moth