The Florida business will most likely not withhold taxes (federal or state) on your services.
You are not considered an employee for your client, which means they are not required to withhold income taxes. However, please keep in mind that as a self-employed taxpayer, your earnings will be subject to self-employment taxes (Social Security and Medicare taxes) at the federal level.
As a single member LLC, you will report the income shown on your 1099 on Schedule C, and remember to include all business expenses.
