We travel all the time with our 14 pound Bichon. We have homes in the US and Sint Maarten. No one ever asks anything and we ignore the island forms, not a problem. We do have the dog checked prior to leaving the US for all vaccinations, etc. and have all her papers. I WOULD NOT submit a form to SXM as you probably won't get an answer within a few months, even if you do, there is no one checking at the airport, never has been (10 years) and probably never will be. We travel 5-6 times a year, no problem.
Don't be spooked, it will go smooth.
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