I don't think the square crop is the best option for the photo given in the first post because it leaves so much empty space around the subject. Debbie gives a good alternative.
Here is another:
I've indicated how this fits a thirds grid. This comes much closer - taking a fresh picture, getting even nearer might be good. However, as Nathan said, it all about making a choice yourself. Try taking a series of photos with square framing in mind to develop your ability to see when it is a good option.
Wulf