Advice with a tenancy contract please?

Okay, so. I moved into my landlord's spare room as a 'lodger' (the legal term, apparently) at the start of August. He permitted me to get a puppy to keep his dog company and, of course, the puppy can be noisy at times, which is an issue for him at night before an early shift/in the morning after he's done a night shift. Long story short, he won't allow me to rectify the issue (puppy needs to be just ignored when he whines at night, which will get worse before it gets better) because it wakes him up and I have to rush down and give puppy attention every time he whines, which is counterproductive.

His dog also attacks mine when mine gets too much attention or gets anywhere near his food, which my landlord hasn't been willing to work on - despite my research and suggestions on how to rectify the situation so that the dogs are happy. Because of his failure to even attempt it, I started looking for other places to live (which he was aware of) a few days before he sent the message described below.

So, on 8th Nov he gave me notice and said "Should we call December the last month? Earlier if it suits both parties?" to which I said, "End of December is fine with me."

The contract we both signed states that the notice period is "One month minimum, two months appreciated."

-question continued in additional info-