How do I get more zebras?

Solution 1:

I already have my first Zebra which I got when I built a ship.

This sounds to me very much like you do not have a zebra. You have instead discovered the zebra race for trading. In order to get an actual zebra joining your village, you will need to play in Iron Will mode (no huts/log houses/mansions built). You will know you've done it right when a Zebra shows up as an actual resource on the left section.

Zebras in Iron Will are a free way to get some small amount of Catpower, which is otherwise impossible without kittens. To make successive Iron Will runs a little easier, every time you reset, your maximum number of zebras will be set to your current zebra count, plus one.

Solution 2:

I've gone through the code and this is the only line that increases the number of zebras you have:

reset: function(){
  ...
  this.karmaZebras = this.resPool.get("zebras").value + 1;
  ...
}

This would seem to imply you get a single zebra each time you reset.