I can transfer my job but the request can take up to 6 months to fully go through. However, I want to purchase the home now. Would I be able to qualify for an FHA loan if I'm here in CT But won't be in FL for about 6 months?

No, you need to wait (at least) until the first mortgage payment will arrive after your first paycheck at the new job location. 

@Skylar Walker you will need to wait at least until your start your position.