Oh fuck is she cute! You know, I made the same accidental mistake when I introduced the new dog to the cats. Actually, I didn't SEE one of the cats lurking but the doggie did. Well, dog went to investigate, cat ran, dog chased. Who can resist chasing a running cat?? It's so much dang fun! It's the thrill of the chase!! I am going to give you another tidbit of (unrequested) advice.
I really think chasing shit gets harder to manage if they are allowed to develop a pattern of chase/run away. From my exhaustive (and exhausting) research on the subject, plus a few hundred bucks spent on a dog behavior lady, I offer the following suggestions: Do whatever you can to not let a chase start in the first place. Things such as keeping Pretty Dog on a leash while cat comes out on kitty's own accord and then, if dog attempts to be overly looky or give a fucking predator style stare, distract her by giving her a known command (like sit) and give her treats (that you will have in your secret pocket) to distract her from the CAT, who is really,
really fun to chase, and to show her that good things happen when kitties come around. Also lavish praise when she attends to you rather than that kitty.
One of my cats was VERY aggressive toward the new dog and it just so happens to be the cat that got chased by her. That cat, FME, has a motto: Fuck with me once, shame on you. Fuck with me twice, well, you ain't gonna get the chance, crackah, because I am gonna kick your fucking ass around the block and back again every time I so much as see your scrawny-busted-up-fake-ass-corgi-wanna-be-looking-self out of the corner of me eye. (Yeah, it's a long motto but it seems to work for her.) Anyway, since this was not a simple introduction any longer, the animal behavior chick said I needed to do something similar to the above mentioned leash introduction or separate them by a baby gate, keeping them very far apart but still able to see one another. You teach them BOTH that good shit happens when the other one is around. Ideally you have two people, one on "cat duty" and one on "dog duty" (Hehe, I said "dog doody"), in theory, each person will maintain the calmness of their assigned animal, with praise and slow, gentle,
calming petting action. Also, this lady was big on treats, so she wanted both kitty AND doggy to receive treats during the "interaction." (I spent as much on fucking treats as I did on the house calls the lady insisted on making.) ANyway, the point of the exercise is not forcing them to get closer but really just being within eyeballing distance. That's all you ask for, and keep it short and sweet, the first couple of times. You eventually,
gradually increase their proximity - same bullshit with the praise, pettings , and treats, of course

- getting them to a point of closeness they can tolerate with out acting the fool.
Again, I know you didn't ask for all this advice: I just feel that I am getting more bang for my buck if I share what the crazy dog behavior lady taught us.
So, I will leave you for now with a big "CONGRATULATIONS" and a request that you continue to update us as your new dog becomes integrated in you household.
PS: I, for one, wouldn't mind looking at a picture of this cat as well.