It's a bit of a tricky situation... So here's the D/L
You can sponsor your husband while you are living outside of Canada, however, in order to be approved as a sponsor, you must prove that you intend to return to Canada with your husband when he gets his PR. This might be hard in your situation, especially because you will have to disclose that you are a full-time student in the caribbean for the next 2 years, they may not believe you intend to come back in the near future (obviously) and may not allow you to sponsor. Having said that, you could try. They ask for "Proof you intend to return to Canada..." and give examples of things like rental lease in Canada (current and future), job invitation letter from Canada showing you have a job to go back to, etc. You will not have these things (most people don't when they're living abroad though). You can say that you are training abroad and intend to return after your training to Canada to practice in your field and give details of how you would do this (ie. My field of study is X. When I complete my training in the caribbean, I will be licensed to do X in Canada. I intend to get a job at X and make a good salary (eg. X) and would be able to support myself and my husband. My field is in demand in Canada and I still consider myself a Canadian, I still pay taxes in Canada, and I am only out of the country for studies in X. If you have a detailed plan about intending to return, they may be ok with that.
As you are applying after October 2012, you are subject to the "new" immigration rule that you must be together for 2+ years after PR to keep the status. This is waived if you have been married for 2 years or have children together. If you have been married less than 2 years with no kids, you need to be together for 2+ years after PR is granted. NOW, after your husband lands as a PR in Canada, he has his status as long as he fills the proper number of days total in Canada to keep his PR status. (This is where it will help you). He does NOT necessarily have to be in Canada for this to happen... He can still count days toward his PR if he is outside of Canada, so long as he is following YOU on a "mission" (ie. school). He could still keep his PR status if he is with you. If, however, he does not want to live in the caribbean with you, lands as a PR in Canada, and you two don't live together in Canada (because you are at school and he is in Canada) then you might have a problem with failing to abide by the new immigration law.
I also am a Canadian citizen who went to school in the caribbean. I opted to wait until I returned to sponsor my partner because it's less messy, even more so now with the new immigration rule. But I can understand that you would not want to wait because you are just starting off (I was almost done over there when I started planning for sponsorship and I lived with him in the caribbean).
Anyway, I hope all of that makes sense. Sorry the answer's not more simple...
Feel free to PM me if you have any questions, since I've kind of been in your shoes.