Toby the rat becomes a Broadway "diva"

At the Ethel Barrymore Theater, their rat problem is not the kind that requires an exterminator. Toby is the rodent star of the hit Broadway play, "The Curious Incident of the Dog in the Night-Time" and has a penchant for having things her own way, reports CBS News' Jamie Wax.

"She's a bit of a diva, so she calls the shots more than I do," the show's lead Alex Sharp said.

Toby plays a pet rat to an autistic boy named Christopher.

"We've grown to love each other a little bit more as time has gone on," Alex said.

Cute critters steal hearts and scenes in the movies all the time. Whether it's a dog like Marley, Babe the pig, Dunston the orangutan or Willy the orca. On Broadway, Sandy from the musical "Annie" is probably the most famous pet to take the stage.

But on stage, unlike in films, there are no retakes, and animals have one shot a night to get it right.

Imagine training kittens to keep their composure amid the chaos on stage in "You Can't Take it With You." In that show, kitten training involves exposing them to loud sounds, and traipsing them about until they are used to almost anything. The regimen was designed by animal trainer Lydia DesRoche, who also happens to train Toby the rat.

To get Toby ready for a performance, DesRoche takes her on backstage tours to help her get acclimated, and the crew acclimated to her.

She's also working on finding a suitable understudy for Toby.

"The biggest challenge was overcoming my fear of rats, which is why I think I'm so obsessed now. It's like you know, it's just so exciting because I'm not afraid of them anymore," DesRoche said.

DesRoche feels that she now really understands rats. You might call her a rat whisperer.

"It's less about [repetition] and more about really listening to the animal and not pushing them too far to knowing when to, you know, knowing when to challenge them, and knowing when to pull back," DesRoche said.

Though Toby spends most of her stage time in a cage, her big moment comes in act two when the cage is opened and she is supposed to kiss Alex. It's said she does the trick eight times out of 10. When CBS News cameras were there, Toby the diva decided a kiss was not in the cards.

"It's a live animal you can't say 'This is your cue, you have to do it.' They don't care," Alex said.

The unpredictability of an animal on stage can be thrilling for the human actors; a chance to test themselves.

"They are completely in the moment. There is nothing about them that's anywhere else than that moment now," Co-star Francesca Faridany said. "That's what we all strive for, for sure, as actors."

Despite the search for a worthy understudy, Toby has still done every Broadway performance of the show.