I would get a separate cage for each kakariki in order to prevent unwanted babies. You'd also need to supervise them when they're outside the cage too, just in case "relations" occur!
Separate cages are generally recommended whether you have two birds of the same species or two totally different species. You just never can tell if two birds will be friendly towards each other in the close confines of a single cage, so it's best that they each have their own safe space to call their own
All advice absolutely right. Definitely don't keep in same cage, get them separate cages, and avoid letting them be together in closed spaces, like Happy huts aka snuggle huts or any type of nesting box.