if you already use it ... and have already spent the money ... do it on the day it runs out.
norton isn't the best choice - it does tend to take a fair amount of processor time ... but it has a better detection rate than avg ... so while I would have said change brands.
(on recent reviews - avira as first, Kaspersky second)
as you seem to already have spent the money ....
I would never suggest swapping an internet security suite
for an inferior free virus scanner.