We can help with selecting the parts for the conversion and with finding the correct gear ratio so it has the top speed and or hill climbing ability that you want it to have.
I understand that the go kart is for a child so it and the driver will be fairly lightweight. Could you tell us a little more about the conversion goals like if the go kart will be used on pavement or dirt, flat ground or to go up hills, top speed, how many miles or minutes it should travel on a single battery charge?
We can gear it for the top speed that you feel is safe and figure out the largest battery pack that will fit in it for the longest ride time. Is it a steel frame go kart, or a plastic ride on toy go kart?
If the kart is geared for a low top speed then the motor will provide most of the braking needed, however a mechanical brake would be needed to bring it to a full stop when going downhill or to stop it quickly. Two AZ1027 wheels could be installed with a chain sprocket on one of them and a brake on the other. MFG Supply has a 4" brake drum that fits AZ1027 wheels on this page: http://www.mfgsupply.com/4-485.html
I notice that MFG Supply has a 48 tooth sprocket that fits the rim you have selected. With this 48 tooth wheel sprocket and a 13 tooth sprocket on the motor the top speed would be 2.5 MPH. Would this be an acceptable top speed or do you want the go kart to go faster?
If you want the kart to go faster than 2.5 MPH then please let me know what speed you would like it to go and I will figure out what size wheel sprocket it needs for that speed, then I can look into having that size wheel sprocket machined to fit the AZ1027 rim.