If you mean that the kit lens you have is the one from the 300D, it won't work on a full frame camera, the usual kit lens from the 5D MkII is the 24 - 105mm IS L f/4 which whilst good is not the fastest lens, so a f/2.8 would be a must for your application, or a fast prime.
You might also consider the 1D MkIV which has amazing high Iso performance, better video than any camera to date, and a brand new auto focus system. The only drawback is the availablity at present and the price of £4.5K which will probably drop to the £2500 of its predecessor.
I have the 5D MkII, and to be honest there are so many reviews about it on line that there's very little point in me adding to them. Friends with Nikons D3 & D700 both conceed picture quality is better, but I'm not convinced that it's comparing like with like. Cameras like the Nikon D3 & D700 are better compared with the 1D MkIII or now the MkIV, the big difference is the strength of the bayer matrix, which is 'weaker' on sports type cameras, giving better high Iso and faster shutter speeds. The D3x has a similar beyer matrix to the 5D MkII, the main advantage being better colour accuracy and saturations.
You really will need to splash the cash on high quality lenses too, because 21MP will really show up the shortcommings, especially with Full Frame. Longer lenses to fill that frame combined with the large apertures you need for low light performance mean that you could be in for quite a large bill! Everything depends on your budget expect to pay around £2800 for the body + a 24 - 70mm f/2.8 lens you will also need a 70 - 200mm f/2.8 IS, another £1400 or perhaps a Sigma 120 - 300mm f/2.8 if you need more reach at £2000.
If those figures are not a problem then go for it! the images you will be able to produce will be as good as is currently possible, however if you budget is a little less generous you might consider the Canon 7D which will perform well with less expesive lenses. Maybe the image quality won't be quite as good as the 5D MkII, but will anyone really notice the difference?
iv'e heard very good things about the canon 7d high iso and low noise
from waht iv'e read about it it's a winner with the highest density pixel count to date
with the latest of canons technology crammed into it which apparently works very well it's got to be on the consideration list
if full frame is a must then it's the canon 5d mk2 both are capable of full hd video
or.. if video is not as much of a concern and low light is a major issue it's got to be the nikon d3 all beit dated but what a wonderfull camera that is