Hi and welcome
In order for you to be able to work here without being a citizen or married to a citizen you are going to have to be hired by a J'can company and I can tell you right now I doubt there will be anything for you. ( the only reason I say that is because being a caregiver doesn't really have special skills and there are alot of J'can caregivers already) The only way you will get a job is if there are no J'cans to fill that spot or that don't have the skill to do it. The company that hires you will have to apply for work permit on your behalf and you may not get it. You can however, come down for 3 mths and extend it to 6 mths and do charity work but you can't work and earn an imcome. And you may have to provide prove that you have the means to support yourself during an extended stay.
Have you checked out the Ministry of Labour website yet? If not, please do, it gives you all sorts of info regarding working in JA. You can also call them and they will be able to answer your questions directly. Just allow the phone to ring and ring and ring...lol Trust me..let it ring.
If I am giving out false info can someone please correct me.