Well, then you're SOL.
Even if you find a carburetor from a junk yard, they may or may not be open on the weekend. That's one problem.
Second, if you order this part from Kahuna or any other dealer, it will take at least 3 business days for them to get it. So you won't get it this weekend.
If you order from BikeBandit, or CheapCycleParts, it takes them either 3 or 5 (can't remember) business days for them to get the part from Kawasaki, THEN they ship it to you. If you use a place like US Address Inc and get it shipped stateside, that means you can maybe get the part within 7 business days. If you ship it to Canada, it will take more like 10-15 business days.
Point is, you won't be able to fix it this weekend unless you get lucky and find it at a junkyard or from someone. Looks like your bike will have to sit for a week and a half regardless. Might as well start tearing it apart, and figuring out what else is wrong. And if you're already ordering parts, might as well figuring out what else needs to be swapped or replaced and get those too. On a 5 year old bike that hasn't been properly maintained, it would make a lot of sense. Do it properly now, and you'll enjoy years of bliss with the bike.
Also, isn't the ZZR600 just a rebadged 99-02 ZX6R or something like that? I likely have the model wrong, but find out, that may be a way to find your spare parts.