It’s perfectly fine to have aspirations and a lot of people I know going through vet school want to eventually work in zoos. Personally I’m very interested in exotic animal medicine and this is definitely my favourite area of vet med. You do have to bear in mind however that at vet school you will have to learn about the main domestic species ie dogs and cats, farm animals and equine and realistically speaking you won’t do a massive amount of work to do with zoo animals (though exotic pets are covered, just in a bit less detail).
I don’t know a massive amount about residencies so I’ll leave that to someone else to answer, but they are definitely not easy to get onto. There are significantly fewer opportunities to work as a vet in a zoo in comparison to first opinion practice, but it’s still possible.
Overall I’d say if you’re certain that you only want to work in a zoo and have no interest in working with or learning any other species group then you should probably reconsider if vet med is definitely what you want to do, but if you’d be happy to also work in practices and with your main domestic species then I’d say go for it.