Can my 2005 pre-runner handle this camper?

I have a 2005 pre-runner automatic transmission,factory tow pkg. 4.0 v-6

I want to buy a 2015 quicksiver vrv 6x15 toy hauler

the camper weighs 3200 dry,My harley weighs 600

I will probably put 400 lbs of gear in camper

when tanks are full that could add another 100 or 200lbs

My wife and I in truck

I think my truck says 6,500 max tow

Thanks for anything I may be forgetting to add in weight wise

 

Should be fine as long as you have a trans fluid cooler on it. I tow a 7x16 enclosed equipment trailer full of tools. My trailer weights in at 6300lbs

 

Yup I have factory tow with trans cooler

 

Should be fine