Julie, please feel free to come and join us at the Plumeria forum whenever you like.
Frangipani is the common name for Plumeria in some parts of the world.
If the Plumeria you just got is only a cutting I would store it until spring. If it is a plant go ahead and plant it in a nice well-draining mix (perlite or sand mixed with the soil will ensure it drains well). While the plant is dormant it will need virtually no water. You may just want to mist it occasionally - I know your humidity is pretty low.
Do not let it get cold AND wet at the same time (so keep it out of the rain if it is below 50 degrees).
There really is no reason why you shouldn't be able to grow this in zone 9b.
Good luck and happy growing!
