Yes, archie follows me round the house like my dog used to, he comes if I call him, and if I have him in bed, he sleeps across my head like my dog did, and he goes absolutely insane if he knows hes going outside. My dog would sit at the door whining and scratching at it, and archie does that, and he gets SO GRUMPY if we dont put him out. Even when its ice outside, he tries to get out there, and as for rain and wind, he doesnt care in the least (though of course we cover the run and give him a hot water bottle etc), it can be lashing down with rain and he just chomps away on the grass not bothered at all.
He also licks my hands like my dog did, and likes to play chase, and he lets me roll him around on the floor when hes stretched out and kiss his tummy like I would do on my dog, and squeeze his lips and flip them around and chew on him gently, and nibble his ears too, I would do that to my dog.
He likes to sit/lie down and watch me till he falls asleep, my dog used to do that too.
I think they share the same spirit, cause years ago, I had a bunny and he let me do those things too.