As long as the quit claim deed is prepared in accordance with laws in county where property lies all you need to do is record the deed in that county regardless of where The holding llc is incorporated. Happy to assist
Just because you are moving to Florida does not necessarily mean that you have to dissolve you old non-Florida LLC and transfer its out of state property to a Florida LLC. There could be good reasons to leave the ownership of the property unchanged. If you are making the change to avoid claims of creditors, it will not work. You should consult an experienced business lawyer to help you decide on the right structure for your Florida business and the best way to deal with your out of state property.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.