I do have another suggestion or two about the go-cart.
You can get a racing frame but most of them are setup for about 1/2 inch of ground clearance.
The alternative is to get one that has the low ground clearance needed when using racing with slick tires but have a second set of larger wheels/tires for off track racing, like in the yard. The tires for home use would not be slicks but actually have some tread similar to a riding lawn mower. More grab for the grass or dirt when it's time for the turns and for stopping/starting. With the right wheel/tire size you will have a couple of inches of ground clearance making the machine much safer for home style or off-road riding. No mowing the grass with the front bumper as would happen with the 1/2 inch clearance when in the racing setup.
The second suggestion is to get a frame that has two engine mounts. That way later as the child gets heaver a second engine can be added for more horse power or possibly for racing. My original go-cart had this kind of frame. No need to buy one with two engines at the start as long as it is setup for you to add one later with out needing someone to weld in a second engine mount.
A year after the crash I was able to ride the go-cart again, after my father had a welding shop add the roll bar, installed a kill switch and added a seat belt. My helmet came from my doctor who told me to wear it or else.
I did have fun with my machine and with the yard size you mentioned the child will also have fun. At the same time the child gets older they should have fun learning how the thing works as well as fixing things as they break, like rebuilding the engine, fixing the clutch and all the rest of the fun things.