If it needs to be a laptop, I would personally recommend getting an ASUS gaming laptop. Something like this should be pretty good for you:
http://www.amazon.com/G750JM-DS71-17...productDetails and fits under the $1500 price range, with some cash to spare.
This one is pretty good too:
http://www.amazon.com/Republic-Gamer...=gaming+laptop but is more expensive.
Either way, don't get sucked into something like Alienware. You spend more for the name. ASUS is expensive, but I haven't had a problem with them. Never tried the Toshiba Qosmio line, but my brother had one that crapped out on him after a few years. Was a decent laptop though.