Hello, I'm a Housekeeping working by myself. Do I need fill out the form DR-405?

Further, visit your county property appraiser's web site (link below) for more information as well as any variations in the method of filing or definition of precisely what is considered to be "tangible personal property".

http://floridarevenue.com/dor/property/appraisers.html

Yes, you are required to file a tangible personal property return if you conduct a business in the state of Florida.  However, if the assessed value of your tangible personal property was $25,000 or less for the prior year, you may be able to file DR-405EZ, Tangible Personal Property Exemption Application and  Return instead.