Why would the autofocus not work, is this always the case with teleconverters or is it something to do with the 28-300 lens?
Both...and the camera as well.
Most cameras need a maximum aperture of at least F5.6 (give or take) in in order to get enough light for the AF to work properly. That's one reason why many zoom lenses have a max aperture of F5.6. The lens is question has a max aperture of F3.5 to 6.3 doesn't it? I'd guess that it would sometimes have trouble with AF when zoomed all the way out.
So, now that we know what the camera needs, we have to consider that a teleconverter steals light. A 2X teleconverter steals about two stops of light. So if you put one behind your F3.5 - 6.3 lens....the camera is only going to get as much light as a F7.1 to F13...which is probably not enough light for the AF system to function.
This is one reason why Canon's teleconverters are made to work only with their top end telephoto lenses. They just won't work well with cheaper lenses.
Another thing to consider is that a teleconverter will degrade the image quality. Of course, some are better than others...but at some point, you would be making a compromise between getting more reach and degrading the image. With a cheaper lens like this, it might not be a great idea to make the image quality any worse.
Another option would be to just do the best you can to get sharp shots with your lens (use a fast shutter speed, use a tripod etc) and then crop the image.