I would say 1 month from tomorrow is 9th January - which actually works out to be a Monday, so you could stipulate your last working day being the Friday - i doubt many would kick up that much of a fuss.
If your contract says 4 weeks notice, then even better, as that would line up with the 6th Jan.
On another note, i think contracts are very poorly worded when they say 1 month, as people can differentiate 1 month as different things - i.e. 4 weeks, 30 days etc. It would be far easier and clearer to all if they just say 4 weeks notice period.