It looks like dyed rabbit "from here," but without feeling it, can't be sure. Although it doesn't look quite as "fluffy" as some rabbit pieces I've seen. But I am by NO means that versed in fur, so....
Offhand, I'd say late 60s into the mid 70s on it, but would love to have a look at the lining. And is that belt original to the coat? What is the shape of the coat without its belt? The shape doesn't look right for the 50s, as it's showing in your photos. Are there any hooks or buttons as closures? Rabbit fur coats were huge in the 70s.