I find NYE traffic across Dubai is generally worse before midnight (say from 9 to 11pm) when everybody is trying to get somewhere and then it picks up again from about 1am for those heading home early. No idea how Airport Rd may be though...
I know this doesn't answer your question per se but maybe get a chauffeur service to pick her up. If you use the Marhaba service you can add that on for about 145aed. You also get the benefit of a speedy service through the airport for her and you can just wait at home and not worry about getting to the airport and back!
my mum is flying in to DXB on NYE around midnight. Superb timing, I know. We live in Mirdif so ordinarily this is a 15 minute drive to terminal 1 to pick her up. obviously traffic is a nightmare on NYE but what is the airport road like? I know it's impossible to tell in advance but maybe someone was in the area last year and can tell me just how bad it was? Not that there's much we can do about it but fore-warned is fore-armed!