This is so nerve-wracking to have a young child so sick. My 4yo grandson recently had a go-round with a stomach virus, possibly on top of a separate respiratory infection. The poor little guy vomited for the better part of two weeks, and visibly lost weight. His parents were poised to rush him to an emergency room, they were so worried. But the advice nurse at his ped's office helped keep them reassured that he was "just" very sick, and would get over it.
Sure enough, after 2 weeks, the barfing stopped, and a week later, he started eating voraciously to regain the lost weight, plus keep up with a growth spurt.
The Pedialite sounds like a good plan. If the fever is gets really high or she shows signs of dehydration, you'll want to get further instructions from the doc's office. I'd be inclined to call them about the lethargy too. That could be unusual, though it may well be that she's just feeling really sick.
Good luck, R.. I hope you'll keep us posted as she recovers.