My start in computing was totally driven by games. There's not many computational problems that you won't hit eventually, so game programming would be a good start to hold her interest I think.
I'd keep it real simple at first. Since vanilla perl isn't graphics oriented I would stick with maybe a simple game like blackjack to start perhaps or maybe even a MadLibs type of program. The both would cover input, conditional logic etc. I don't think you want to go to far, right off the bat.
I don't know if anybody here remembers Gorilla that shipped with QuickBasic but that might be a good second project. It's simple but fun.
"To be civilized is to deny one's nature."
Re: Junior Perl
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Games sound good – I remember a program that guessed what animal you were thinking of by asking a series of questions (has it got four legs?, wings etc.) – it also had the ability to learn about new animals and would fit them into its classification tree. I guess something like that would introduce all the programming concepts pretty quickly and yet still be fun