What focal lengths do you find most effective for your pet and people shooting? You may find that adding a lower cost prime lens, either f/1.4 or 1.8 at that focal length would be a cost effective move, when getting the D7000. The D600 is more capable but to get the most out of it will require a commitment to growing a pricey lens collection. For people shots I like the 70-200 on either DX or FX. It just works for my desired perspective of people shooting and it does very well indeed on the D7000. Adding 85 1.8G would give low light shooting a real boost and is a good head, head and shoulder portrait lens.
I really like the D7000, it does everything very well but I also have the D800 which means the D7000 gets a little lonely in the camera bag, waiting for the next time I give it some exercise. I had a chance to use both Saturday night for a large formal social event at a private home, where the guest list included 2 ambassadors, the entire board of directors of a F/500 company and various opera and ballet stars. I took my bag just in case the pro hired needed some assistance. Well, he never showed up. I got 450 shots with the 800 and 250 with the 7000 and both did a fine job. There were no shots that I had regretted not using the D800 on it. We had performances in the ballroom by principle dancers of the Mariinsky Theater and a mini-opera that had a lot of non-opera fans change their mind. The women were going weak kneed over the male singer who was not only excellent but right out of central casting for the leading man or model. The female singer was stunning, in both voice and beauty. I'll post some photos taken later. I am heading out the door to fly to California.... I mentioned all this because both cameras are excellent and have strong points that fit right into your chosen subject matter. I would not hesitate to recommend the D7000 if the D600 and its lens was a stretch.