It appears that you have done the right thing so far in responding in writing with an objection to the charges. If you have pictures from your move out, that could be helpful if you have to prove to a judge that the carpet did not have to be replaced. You should take all the documents to a landlord-tenant attorney to determine whether your objection was done properly and if the landlord followed procedure. If you hire an attorney and you are able to recover your security deposit, the landlord may have to pay for your attorney's fees also.
A carpet generally has a 5-yr lifespan, and if it has to be replaced, the landlord should pro-rate based on how old the carpet is. It's similar to having to repaint the walls. How long were you a tenant at this place and do you know how old the carpet is?
Assuming you filed your objection to the landlord's claim against your security deposit in accordance with F.S. 83.49(3), and you believe strongly that the charges assessed are incorrect or unjustified, you would need to file a small claims action (assuming the damages are $5K or less) for the court to adjudicate who is entitled to the deposit funds. However, first I would try to work it out with the landlord to see if you can come to a mutual agreement. If not, then one of you needs to file an action with the court to see who is to get all or part of the funds.
If you think the landlord has a practice of taking advantage of tenants, I would get with an attorney to discuss first before filing. A properly worded letter from an attorney to the landlord on what is about to happen might get the landlord to just drop the matter and return all of your funds. Just the mere threat that you are going to request to review all tenant files from the landlord going back 3 yrs is enough of a deterrent to drop the matter and return your deposit.