Legal Question in Landlord & Tenant Law in Florida

No. Your letter is notice, as long as you included in your letter the important things - when you will be vacating, a forwarding address, the disposition of the keys and anything else that might come with the apartment (garage door openers, gate access cards, claim for the security deposit, etc). I assume you mailed the letter to the address specified in the lease within the time required. But even if you didn't, there's no legal requirement that you have a specific form of a notice to vacate.

What does your lease provide in terms of notices? if there is no specific requirement in your lease, I agree with mr. kaufman that there is no specific requirement for a "notice of intent" or that the notice cannot also be in the form of a letter. if they have a form they want, I would suggest you ask them for that and see if you can agree to the terms.