Out of state license and LLC?
Yours is an interesting case. I presume the manufacturing business in Florida was already registered in that state, and you intend to form a new, separate business (online retailer). If that is the case then you might want to register it in the state where you would be running it from, which in your case I believe is Missouri.
There are merits of registering an online business in one of incorporation heavens such as Delaware or Wyoming, however, even an online business is run from somewhere, and if this somewhere is in another state then you as the person running it would want to enjoy the benefits of the expenses you can deduct from the business income, dealing with maintaining an office in your state. In that case registering in your state would be necessary anyway.
Its important to note that since the product you sell would be shipped from Florida you would need to collect sales tax from Florida residents (as well as from Missouri residents).