Dog getting along with cat day 1?

So long story short, I took in a dog that was abandoned. Shes really sweet & is very VERY calm. Like she can have another dog in her face checking her out and she doesnt even growl. Shes 1 & I believe shes a pit mix but I’m not 100% sure.

So anyways, I noticed when I brought her to the vet, she didn’t even mind the cats. One would walk in and she would sniff towards it, but there was 0 aggression. She would ignore them half the time or just look at them.

So I have a black cat named madam, and she normally likes to be alone. The moment I brought Luna (my dog) in, Madam was instantly sniffing her & curious about her. Luna was very unsure but just sat down and sniffed her back.

The cat has jumped on Luna & she doesn’t react much besides leaning up and looking at her like “what the hell? “. She laid beside me all night & Madam has been in and out of the room but she hasn’t reacted at all. Shes actually right now sleeping under the blankets while madam is on top of me.

My question is, should I be worried? Madam is my baby & I don’t want either of them getting hurt. I keep a close eye on the both of them but the entire time they acted like they knew each other their whole lives & past lives. Hell madam cant stand other cats (she will hide from them) but she just accepted Luna instantly.