Javier,
The stated 5.8 amp output will barely keep your batteries topped off. I don't see you getting a lot of other use out of this rig.......just isn't enough juice coming out of it!
And in South FL in the summer in the rain.......there ain't no sunshine baby!!!!
Better go with a gen-set that can power your A/C. If you intend to keep it running a long time, go for the 3KW Honda or Yamaha.
............possibly converted to LP fuel.