Go nowhere near a knitting needle 
Really, nothing down a cast except the limb it's for, ever!
I do agree with the multi-pillow-proppage though. You can get special bags for over the cast, but for a quick shower (rather than swimming) a bin bag taped well should be fine. (Not an ordinary plastic bag as the childproof holes will stop it being waterproof enough) Any softening of the cast or damage and head straight back to the plaster room at the hospital (any hospital will sort it for you if away from home etc)
She can do anything she can do - she'll find out what's comfortable. Being in the cast supports the break, so she won't be able to do any damage to it as it heals.
Encourage her to keep it up especially at night, and to keep moving her fingers to stop it swelling up as that tends to be the uncomfy bit.
Keep a note of any worries or queries over the next few days though, and take it along to fracture clinic. I'm assuming you've only done the A&E bit so far; you'll get seen by the orthopaedic team in the next few days, and a plan eg timescale from that review of how she is and what her XR was like. She'll likely get a news cast that day too - if lightweight cast, go for a bright colour - the white looks foul far quicker. Sharpie type markers are pretty much the only thing to write on that stuff with though - or a few stickers??
At 3 it's going to heal up really quickly, and she'll be back to normal in no time, though. Kids really do take this sort of thing in their stride, she'll be fine.