I must admit, I had never heard of Gambian Giant Rats. Now, they're a major health hazard, along with pet prairie dogs:

These rats can make wonderful pets. They are intelligent, social and can be very gentle if handled from an early age. They play-wrestle like domestic rats and many seem to love to be cuddled, petted and pampered. They seem attracted to shiny objects and will try to remove jewelry and watches. I've heard of one that has a stuffed toy lion it sleeps and plays with, oddly enough without chewing it to pieces like a domestic rat would. . . .

They are not pets for everyone, requiring patience and understanding of their habits. They grow to the size of a small cat and cannot be 'punished' like cats or dogs when they do something wrong, requiring more gentle means, such as tone of voice (a loud OUCH when a baby nips too hard can make them pause, much like when a rat nips another in play too hard and the nipped one SQUEAKS and moves away (or nips back, except as humans we are not equipped to do this), ending play!) and behavioral methods, working around their natural behavior.

This might be a good time for a re-release of the old film Ben.