I can't recall the exact picture, but if it is what I think it is, then it's actually an illustration from another children's book of the same era (possibly same author or illustrator). The name of the book is "The Runaway Bunny." Story goes something like this: Kid bunny tells Mom bunny one night that he's going to run away, and Mom counters with how she will find Kid in spite of it all.
"I will become a fish and swim far away from you." "Then I will become a fisherman and catch you with my net, because you are my little bunny and I love you."
"The Runaway Bunny" is a marvelous book, btw. There was a copy of it at my grandmother's house on Cape Cod, and I think my brother and I must have read it hundreds of times. Great, reaffirming story about how parents will always love their kids, and beautiful (if slightly surreal) illustrations with the baby and mother bunny becoming a fish and a fisherman, a sailboat (with enlarged bunny ears for the sails!) and the wind, etc. Amazon link to hardback edition here - pity they don't show the illustrations!
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"I will become a fish and swim far away from you."
"Then I will become a fisherman and catch you with my net, because you are my little bunny and I love you."
et cetera.
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