I really like this song.
Just some stylistic recommendations
I think Miezi should be "kitty" (Kitten means a baby cat, but kitty can mean any cat). Sounds more kid-like, and works better with MieziKatze, since we say "kitty cat" in English.
And "kick" instead of "step"
with "a" boot, or "your boot"
Cat-hating or "cate-hate" would sound better than "hating of cats". imo.
This song has very simple language on purpose. It's meant to be from the viewpoint of a protagonist that is allergic to cats - and well, resolves to killing cats as a solution.
I have no idea what the "has" part in the title and chorus means, it's probably just there for the rhyme.
A lot of the intentional jokes in this song come from the language and words used, it's almost poetic (if you're a really disturbed poet that is...) and thus very hard to translate appropriately...