A FHA lender must look at your past two-year work history. You will need to explain any gaps in your work history.
According to the FHA guidelines, "To be eligible for a mortgage, FHA does not require a minimum length of time that a borrower must have held a position of employment. However, the lender must verify the borrower’s employment for the most recent two full years, and the borrower must:
* explain any gaps in employment that span one or more months, and
* indicate if he/she was in school or the military during the most recent two full years, providing evidence supporting this claim, such as college transcripts, or discharge papers.
Allowances can be made for seasonal employment, typical for the building trades and agriculture, if documented by the lender".
Based on your case, it seems unlikely that you would be disqualified from a FHA loan based on a short gap in your employment history. The FHA does not require an explanation for a short-term gap of less than one month; however, your lender can request additional information. The lender will most definitely evaluate your situation and determine the stability of your income and the amount of mortgage that you can afford to repay each month.