With a planet full of Kryptonians to make up his army, why does Zod need Doomsday?
Because it’s the ultimate sign of power, and Zod pathologically needs everyone to bend to his will.
It’s also like having the equivalent of an atomic bomb. Sure, you’ve got the numbers and vehicles and armaments, but also having the most powerful, devastating weapon in your arsenal is going to help you win a war on Krypton
You can bet Zod will keep his army away from planets with yellow suns, can’t have rebels with super powers.
He doesn’t know if planets under a different sun will handicap his army.
Doomsday is Doomsday wherever he goes
Why bother with an army when you can just throw doomsday at them however many times you need till he gets the job done