Unfortunately most 'compact' cameras with smaller sensors don't do so well at high ISO - there's a lot of noise - and this is one area where DSLRs win out. You may find that the images are fairly noisy even at ISO 200, and barely usable at ISO 400, whereas with the larger sensors on a DSLR the noise doesn't become very noticeable until ISO 800 or above.
There's no way around this really, and it limits the low-light abilities of cameras with smaller sensors. Things are improving on some of the latest models, but if low-light shooting is important then I'd put a DSLR on your Christmas wish-list.
