Well, you will need at least 1-2 years of experience as an RN in your specialty before you travel. Once you have the experience, you'll be ready to hit the road!
For a dog that weighs 40lbs, most airlines would probably not let you bring them in the cabin in a carrier (especially 2 of them), because they are too big- their carrier would not fit under a seat. So, I think they then do go in an area under the plane (not necessarily by the luggage) that is climate controlled & pressurized. You need to have paperwork completed by your vet beforehand stating that your dog has had all their vaccinations & is fit to fly.
I have not seen any 24hr/week contracts. Most are 36-48hrs/week. You could work 24hr/week as a per diem or agency staff, but then you would most likely not get housing or travel reimbursement.