One month will not likely interfere with you ability to process dairy. You may find you feel and perform much better without the milk, though. Many, many people who have completed one or more Whole30 programs consume dairy products occasionally afterward. I wouldn't advise it, but that's me.

While I am a huge fan of whole foods, dairy is an excellent source of protein and other nutrients. If you are concerned about dairy then give this article a read. http://dairydelivers.wordpress.com/2012/07/15/understanding-lactose-intolerance/

I don't think you should have any problem. I didn't drink milk for over ten years (nothing will turn a kid off of it like making them drink four glasses of lukewarm milk that's been sitting out all day) didn't use butter, yogurt maybe only a couple of times a year after I was 18. Went back to it about a year ago, because I was having starvation problems and I couldn't eat much solid, and have had no problems. I'm of mostly mid-European descent (German and Basque) so I am probably genetically inclined to lactose tolerance.

I now drink 1-2 gallons of whole milk (usually raw) per week in addition to my small cheese, homemade greek yogurt, and butter intake.

I've done two whole30 challenges and both times was able to go back to having butter and heavy whipping cream with no real problems. That's really the only dairy I have except for occasional Greek yogurt and a little cheese now and then. I think you should be fine if you tolerate it fine already.

I didn't have any dairy - not even ghee, for a year and a half and I've recently starting eating it again. I have goat cheese and yogurt everyday with zero problems. I never drank milk to begin with, so I don't know about that.