***** NOT A TEACHER *****
Your question fascinated me so much that I did some googling.
I discovered that this children's story (for children and adults) is so charming that it may be made into a motion picture.
To answer your question, I believe that one must know a little more about the story:
1. Frip is a village.
2. Three familes live there: the Romos, the Ronsens, and Capable with her dad.
3. Gappers are little creatures that attach to goats and prevent the goats from giving milk.
4. The children of the three families spend all day pulling the gappers off the goats.
5. One day the gappers decide to attack ONLY the goats of Capable.
6. The two other familes refuse to help her. They say something like: "Well, since you are now the only victim, you must be doing something wrong. And we must be doing something right."
Therefore, in my opinion, when Sid says, "I certainly wouldn't start fishing about it," I take it to mean something like: "The gappers are attacking your goats. The solution to your problem ["about it"] is NOT to start fishing." Sid tells her to "work smarter. Be more efficient." He is telling her that the gappers no longer bother her neighbors' goats because her neighbors are apparently smart and efficient.
She ignores them and does start to fish.
And, of course, the gappers then start attacking the goats of her neighbors!
P.S. If another member shows that I am wrong, I (or a moderator) will, of course, immediately delete this post.