If you are looking to tow a heavy RV and that is the sole reason to switch, you are better off putting that money into a few year old diesel pick up truck. No one has attempted the diesel swap. Many people have done the Supercharger. It would help with towing.
Your statement "How many extra milles can I do with a supercharger ?" is ambiguous. Are you referring to MPH, MPG, miles per tank??? The supercharger actually gives your worse fuel economy than stock.
Ah, okay. You do not need more power to tow (only people that think this are the macho guys trying to compensate because it takes longer than 10 seconds to get to 60 hauling a huge trailer) The FJ has enough power. Your problems towing heavy objects is the size of the FJ. A small vehicle towing a large trailer will get pushed around by the trailer. It has a max towing capacity of 5000. So include yourself, whoever is with you, gear, subtract that weight from the 5000 and that leaves what you can tow. 4600 should be okay though.
Make sure the tongue weight is no more than 500 lbs, and don't even think about towing this trailer unless it has trailer brakes.
supercharger WILL help you with the MPG. It'll be a big help in lugging that big RV. Your other option is too regear your tranny to a more of an aggressive ratio, which will give you more power and slightly better MPG.
How many miles will you be towing that RV trailer ?
Wind resistance is a big factor when towing RV and cargo trailers at highway speeds.
My opinion: If you are towing short distances, save your money and use the FJ as is. If any mileage is gained with the supercharger it will be so minimal that justification on this basis is nearly impossible. If you are towing long distances, buy a decent used truck (diesel is preferable) for a tow vehicle.