As another person said, you can buy cheap basic motorised platforms from such Chinese sites.
I use banggood.com myself and get loads of stuff from there; H-bridges, ESCs, motors, components, sensors, bench power supplies, oscilloscopes etc. basically anything except batteries which are a problem here since we live in Europe and there are a lot of safety standards.
For instance here is a motor and wheel assembly for 3 dollars: http://www.banggood.com/Robot-Smart-Car-Wheel-Deceleration-DC-Motor-For-Arduino-Smart-Car-p-907973.html?currency=USD
And here is a whole kit for 10 dollars. http://www.banggood.com/Smart-Robot-Car-Chassis-Kit-Speed-Encoder-Battery-Box-For-Arduino-p-915324.html
As for reliability, I can confirm that everything I order arrives safely and payment can be made through paypal so is pretty much safe also. The only catch is the basic delivery period (free shipping!) takes up to 27 days. Some items offer expedited shipping for a charge and that gets a bit weird because sometimes it is just a couple of dollars and the item arrives in a few days.
Mind you I would not trust my life to anything sourced from such places because quality is not always the best (for instance an imitation Arduino may have some parts not perfectly aligned), but for fun stuff its great.
So I would highly recommend it. Hope that helps!
By the way if you want to make it more fun you might want to incorporate a laser (make sure it points downwards just ahead of the vehicle. In that way the cat will tend to spring at the spot rather than the vehicle!) if you want to do this for free, get an old DVD drive (not CD) and dismantle it to get the 3 lead diode.
Say hi to your cat for me. :-)