Lisanicolet,
First of all, welcome to the board! You will find an amazing amount of great people and information here, glad to have you join us!
The question you ask is one that often is thought of by many of our visitors to Jamaica. You are definitely not alone. But, there are many legal and economic issues that you need to be aware of regarding working in Jamaica.
While there are a few exceptions, whenever a foreigner wants to work in Jamaica, be it as a volunteer, in exchange for room/board or for pay, you will need to apply and be granted a work permit by the government of Jamaica. This is the same as virtually every country on the planet, Jamaica is no different in that regard. The current cost to apply for the permit is approx. $160us and the fee for the actual permit would be a minimum of about us$300 for a three month permit. The employer generally would pay this amount - but in your case, you may be the one to have to foot that bill.
Besides this legal issue, there is the economic issues to remember. As a foreigner working in Jamaica, there is usually some skill that you posses that a Jamaican would not in order to be granted the work permit. The point of the permit system is to insure that Jamaicans are given the chance for the job you would be doing. Allowing a paying job to be taken away from a resident of any developing country is not a very good thing for that country to do - it makes no economic sense.