you don't need a gaming computer to play WoW. I believe any of today's PCs would play it well.
Even my 7 years old computer can play WoW just with it's integrated graphics card and the shared graphics memory.
WoW (2005) :
# Config minimum : Win 98/2000/ME/XP, PIII 800 MHz, 256 Mo de RAM, carte 3D 32 Mo, connexion internet 56K
# Config conseillée : Win 98/2000/ME/XP, PIV 1,5 GHz, 1 Go de RAM, carte 3D 64 Mo compatible vertex & pixel shader, connexion internet 512K
WoW The Burning Crusade (2007) :
# Config minimum : Win 2000/XP, PIII 800 MHz, 512 Mo de RAM, carte 3D 32 Mo, 10 Go de libre sur le disque dur, necessite World of Warcraft pour fonctionner
# Config conseillée : Win 2000/XP, PIV 1,5 GHz, 1 Go de RAM, carte 3D 64 Mo
WoW Wrath of the Lich King (november 2008) :
# Config minimum : Windows XP/Vista, processeur 1,3 Ghz, 512 Mo de Ram (1 Go sous Vista), carte graphique 32 Mo gérant le transform & lightning, 15 Go d'espace libre sur le disque dur
# Config conseillée : Windows XP/Vista, processeur dual core, 1 Go de Ram (2 Go sous Vista), carte graphique 128 Mo gérant les vertex et pixel shaders, 15 Go d'espace libre sur le disque dur
conseillee = recommended (it's in frensh, but I think you are clever enough to understand it, I just translated one word for you, except that the rest is similar to english)
In case you want a real gaming laptop (but it's gonna cost ya) check AlienWare LapTops Made just for real gamers ;)