However you end up building your training cart, be sure to learn about harness recommendations to ensure that weight is distributed safely. Weight pull harnesses have a thick collar that is in effect a heavily padded yoke. There is a spreader behind the dog in lieu of shafts. I haven't personally done carting but the same principles should apply for distribution of tension and weight. Here are some images of different types of carts with dogs hooked up: cartingequipment
You want a well-fitted harness first. There are different types depending on the type of cart and how dog will be hooked up.
Always start light when you begin training--the idea is mostly about getting the dog used to pulling something behind them. The empty cooler cart should work well for getting started.
For the weight pull training we did, I also strung together some beer cans to use as distraction (noise) training. I don't drink much beer so my friends enjoyed helping make the rattle-drag, LOL.