Help to ID a Children's book

Hi, I dont remember the name of the book so hopefully the details i remember help others to identify it. It was from 1980's-early 1990's? children's picture book about a Rabbit/Hare who lives with his parents. He leaves his home because he likes to eat meat? crosses bushland ends up at a Zoo and tries to live with Lions it doesn't work out so he moves on. He finally meets a Dog they become friends and i remember a distinct last drawing of them looking at the reader both standing up on two feet smiling. The dogs house was in the background. It was in colour about A4 size and the art was very distinctive. The Rabbit/Hare walked on his two back feet and was very tall and brown/greyish in colour. Hopefully someone can identify this books name. Thanks in advance.