Собака бывает кусачей

"What makes a dog fierce"

"Никто не съедает гражданку Лошадку
И с ней гражданина Кота,"

Nobody devour Ms. Horse
Along with Mr. Cat

(Actually "Citizen," which in USSR was an equivalent of "Mr./Ms.")

"Ведь ей не везёт в этой жизни ужасно,
Ужасно как ей не везёт."

As she is unlucky in this life
She is horribly unlucky.

"Но шутки с бродячей Собакой бездомной
Опасны, особенно полночью тёмной -
Вот самый собачий,вот самый огромный,
Огромный собачий секрет."

But meeting roving homeless Dog
Makes you nothing good, especially in the dark midnight.
That is the very doggish, the very grave,
Grave doggish secret.

(The secret refers to all that was in the song: "The dog is nasty because she is treated nasty.")