The good news is lenders can approve you for a loan with your NY income as long as your credit scores, debt to income ratio, etc. qualify you. The bad news is if you are not moving into this home within 60 days after closing, this loan will be considered an investment property loan and you will be subject to higher interest rates, higher lender fees and a larger down payment. You can refinance after you move in but there are lender & closing costs for refinancing. Therefore, you are paying the same costs twice and that is expensive.
Is your transfer guaranteed? Make sure because employees can be told of a transfer, then it falls thru. If I were you, I would rent or stay at your sister's home AFTER the transfer is final and you move to Florida. By that time your husband hopefully will be employed, then you can use both incomes to buy a home. If your husband is an employee and will receive a W2, lenders just need 1 month of pay stubs because W2 income is easily verified by computer. Workers who are independent contractors, self employed or receive a 1099 need 2 years income + tax returns because lenders cannot easily verify their income.
Tell your husband to get a job where he will get a W2.