Mudflap is a cat stalker, but she and Elli looove each other and sometimes the cat will stalk her too.
Mud is not aggressive with her at all, and I can easily get her to stop stalking the cat so it's not an issue.
You're already off to a good start. For a lot of BCs, nothing beats herding. It's the best thing on the planet. But if she does have a toy obsession, or is very food motivated, or has a very good recall, start using this to make her realize that toys/food/you are SOOO much more interesting than the cat.
Zeke, my BC/ACD has been terrible with cats from the first day I brought him home at 12 weeks old. He was abnormally focused on them, aggressive(in a stock aggressive
kind of way, herding behavior...but is very much a no-nonsense type herder, NOTHING is going to get past him and stock of any kind is going to do exactly what he wants OR ELSE!), generally very obsessed. My poor cat Elli, she's been around dogs since the day she was born and has never been around a dog that didn't like cats. I'm thoroughly convinced she thinks she's a dog. So she is excellent with dogs....but the poor thing is intellectually challenged, and does not read Zeke's signs that he wants to chase her. If I let her she would bat at him, rub on him, kiss him, etc just like she does Mudflap. And of course she would pay, because Z isn't in a place to be able to tolerate that from her and I don't think he ever will be.
Anyway...I started at Petsmart, which may not the best idea...I was actually working with other issues(he is very fearful of strangers) and realized I could work with the cat issue there as well every time we passed the adoption center.
At Petsmart, I started on one side of the store where he could have seen the cats across the aisle but wasn't tempted to look that way because they were so far away. We would heel, do tricks, etc here. We gradually shrunk the gap between Z and the kitties. Another important part is that I would stand somewhat between Z and the cats, but off to the side so he could still see them but I could sort of keep him from just totally focusing on them. I asked for a trick, he did it, and I would roll his tennis ball away from the cats so he had to turn around and run the opposite direction. (Z is also tennis ball obsessed, he is not food motivated. If your dog is food motivated, you would just toss a treat behind your dog.) It took a few weeks to be able to get to that side of the store and not lose Zeke when he saw the cats. We just kept shrinking the gap, and I kept making him run away from the cats(when I don't death stare the cats, I get to chase my tennis ball). When he got really, really good with this(could be right in front of the adoption center without death staring the cats), I would have him sit-stay right in front of the adoption center, with his back to it, and I would call him away from the cats. Or I would have him sit-stay on one end of the adoption center and call him from the other end of the adoption center so he had to walk in front of aaalll the cats to come to me. (***Long leash is a must.)
He is still very obsessed with cats, but I can now call him away from cats very easily and he is not locked on every time he sees a cat. I still cannot just trust him alone with my cat; we are still working on it. But, I can at least break his focus now. I used to have to literally drag him away and even when we were 15 feet away he was still death staring and completely unaware of anything that was going on other than CATS.
If you can keep your kitty safe and separated from your dog, but still VISIBLE, you could try something like this exercise.