Some WD hitches require drilling, some don't. I would be more concerned about sway control rather than WD with your setup. Some WD hitches have sway control built in, but the cheap ones don't. I would also recommend investigating towing with air suspension, if you have it.
There is a good chance you will end up over the GVWR of the trailer. The tires are probably barely rated to meet the GVWR. A blowout with a single axle could be nasty. I would consider upgrading the tires (assuming they have a low load rating). Weighing the trailer couldn't hurt either.
Otherwise, your setup should be awesome. It will take time to get the hang of it, but I'm sure you'll do fine.