World of Warcraft should play on your laptop if the graphics chipset is up to it and is supported by it.
The only way to definatly answer it would be if someone else had the same laptop and it worked on his/hers.
Its the graphics that might be the stumbling block. Your laptop appears to exceed the rest of the requirements comfortably.
Regarding a desktop have a look at the Novatech ones click here some of the cheaper ones should meet your requirements but you would have to add on the cost of a monitor and another £60 for a reasonable graphics card.