The OP has stated that he will be carrying 1 quad (1st post), then 2 quads (another post). If only 1 quad located close to the camper (away from the tongue), then 800 lb. bars would probably suffice.
2 quads @ 700 lb. each placed on the platform (which appears to be centered between the axles and tongue) is going to put ~700 lbs on the axles and tongue. 1000 or 1200 lb. spring bars would be needed if that were the case.
The OP does not state what kind of WDH is going to be used. Equal-i-zer "spring" bars don't appear to be actual spring steel....the bend very little or none at all. Some members have even posted that Equal-i-zer tells them that using oversized bars is not a problem. There is little of no shock absorbed when using an Equal-i-zer......the trailer and TV suspension takes it all.
Other WDHs have true spring steel in the bars, where some of the road shock is 1st absorbed by the bars, then distributed to the trailer and TV. In the case of a WDH with true spring steel, sizing would be important to give you best ride.
When initially getting my trailer set up, I tried 1200 lb spring bars, and the ride was much too stiff. I went to 800 lb bars with my 700 lb. tongue weight, and the ride is much better.
You can see the bend in the bars: