Just wondering if my computer can handle World of Warcraft's software will I be able to play Star Wars the Old Republic without a problem?

It depends on how well it can play World of Warcraft. Are you able to play it at max settings, or do you have to tone them down a lot? The Old Republic is a lot more resource heavy. I can play WoW on my laptop, but I can not play SWtoR on it. With that said, I can only play WoW at low settings on it. If you can play WoW at max settings, then you should at least be able to play SWtoR at low to mid settings.