laptop upgrade help

i started playing skyrim and boy am i addicted. thing is i want to play the game to its full potential. i am currently playing on HIGH default settings. anything higher than that and my game has a one second lag response time.

i currntly run sager laptop with intel i7@2.0ghz, GPU is nvidia 460m@1.5gb with 4gb ram@1333. i am looking to upgarde my CPU/GPU with the following: intel i7@2.4ghz and gpu will be nvidia 580M
@2gb. both together will cost close to or over $1000.

i'm asking the publics' opinion on whether i should get both upgardes or just one of them. my laptop can run most demanding games: i.e BF3 and skyrim but the DX11 settings slows my system down. so with that said is it a CPU issue or a GPU ???

thanks in advance:D

thanks for the reply. turned out that my gpu shared some of my sytem ram leaving me with 2.3gb of ram for software. i bought a 4gb stick and have it installed already giving me 6gb of ram for my software. game runs smoother on ultra but i still have a half second lag between my keystrokes and the character movement but it only happens on ultra setting. it may be the ultra shadow setings or 16xAA setting. before i had it dropped to 8xAA and shadows on high and my character speed was faster in response.

anyway i may stay with my 460 gtx gpu since i don't believe 2012 has games that will push my system settings, unless there is a crysis 3, bf4 etc. i work and live overseas so desktops are not in my plans and as for a new laptop, i'd be better off upgrading my system to a 580 gtx for $700 as oppose to buying a new system with the same card for $2000

thanks for the input