How long until...

my dog will settle down and like our new kitten. Heres the background, we have a 60lb 1yr old lab/rottie fixed female. Shes quite energetic and when she sees cats outside she wants to play so badly. She doesnt bark or growl, just crouches into play position and whines at them. We brought home a 10 week old kitten 4 days ago and the cat is great. He was raised around dogs so has no fear of our pup and stays very calm. We are actually able to get our dog to sit at attention while we bring the cat right up to her and although she whines and basically vibrates she will sit still. We currently have kitty in the back half of the house with dog in front half with a baby gate separating them. Kitty however, must have a death wish. He keeps jumping the gate and wanting to explore the living room. He's pretty quick too. I'm not concerned that puppy will want to do her harm, just that she will play too rough and grab kitty and shake him (like she does a stuffed toy when she gets ahold of them) She seems so fixated on the cat and whines at the gate when she cant see him.

How long will this go on? Will she eventually calm down around him?

Hi cmartin and welcome back. I don't have any current dog/kitty experience, but I would not recommend that the two be left unsupervised (obviously), and that the dog should have a leash attached when she is interacting with kitty for a while. That way if she acts incorrectly you could grab the leash and correct her quickly. I can understand your concern that the dog may accidentally play too rough and injure the cat, it's a serious concern. I'm sure others with more experience will be along with more ideas.
Good luck to you.