I don't discount anyone else's experiences with acceleration, but I do think there is a difference between asking a 9-year-old to work really, really hard and asking a 6-year-old. It's one thing if the 6-year-old WANTS to spend a huge amount of time on homework. If she doesn't, then IMHO it's not fair to insist on it.
The other thing that I think people are overlooking (or perhaps I misread the OP's original post), but I believe that this is a full-time gifted program. This 6-year-old is being asked to keep up with GIFTED 2nd graders. I don't how advanced the program really is, but it doesn't sound like it's the same situation as a one-year skip in a regular non-gifted program.
In a way, it's ironic that I'm saying all of this, because I am a huge proponent of having kids develop "grit." I just think that it sounds like the grade skip was too much too soon, and I do see a downside to making a kid struggle so much this early in her school career.