I was the same! I would recommend speaking with your local GP about vaccination requirements for the above countries. I did this a couple of days ago with my GP in New Zealand. I had to get Typhoid, Polio. Booked in to see a Travel Doctor in a couple of weeks to get Yellow Fever, then to see if need Meningitis and Rabies? Definitely just call your local GP and ask to speak with a nurse, or see a doctor and they should give you some guidance.
In regards to visa information. I did a quick search on the web, and it seems NZ passport holders require visas for Kenya, Tanzania and Zambia. For NZ passport holders, it seems these can all be obtained on arrival. I hope these can easily be obtained while on the top deck tour itself
Hope this helps a little. I am booked on the 31 day trip starting 30 Dec. Are you booked on one yet?