Sim kittens and puppies spring into existance at roughly the equivalent of 8-12 weeks old. Old enough to be eating solid food and separated from their mothers (if you want to adopt them out) Yes, they will continue to nurse as long as mama will allow, but they don't have to, and it may not be enough anyway.
If sims 4 pets had a "newborn" stage, I'd agree they should be nursing in some way, but they don't. And if they added it, I can't see it lasting more than 1 sim day on Normal Life Span, so I'm not sure it's worth the effort.
