I'm doing this without much dairy. A little raw cheese every other week is about it. I know I don't need the cheese, but since I seem to tolerate the raw cheese, and I REALLY love cheese - I'm allowing it. I'm using mostly coconut milk, coconut oil, tallow, eggs, avocado, bacon, organ meats and poultry and fish, and some leafy greens for good measure.
I've given up on keto-stix because even when I'm dropping body fat fast, have stinky-tones and no appetite, I pee negative to trace at best.
Just saying, power to you, you can do this without dairy.
Steak, eggs, potatoes - fruits, nuts, berries and forage. Coconut milk and potent herbs and spices. Tea instead of coffee now and teeny amounts of kelp daily. Let's see how this does! Not really had dairy much, and gut seems better for it.