I been thinking about this.
Does she want a bigger machine? Experience tells me that as soon as a kid can throw the machine around (instead of the machine throwing the rider) a parent thinks they need a bigger machine.
Under the circumstances I think she'll be scared of a bigger machine.
When we started racing the 90cc class was what you did till 16 years old. All the kids never noticed how big they were on them. They raced and had fun. I have built many motor for adult ridden pit bikes. Let's face it, adults like the mini's. They are fun.
My opinion, keep the polaris at least till she's confident and don't need to be encouraged to go faster. Rider size isn't a issue. Ability's are.

 

That's a good point. It does sound like she's quite a timid rider at this point. Having a larger, faster, more powerful machine might simply scare her. I was riding a while back with a group of people and one of them was a girl of similar age. She was on a Honda Recon and she was not scared at all of the machine. She was sliding around corners and really throwing the machine around. Ok, she might have been a a little older, maybe 13 or 14 but the point is, if she had something more powerful, she would not have been intimidated by it. I had my Grizzly at the time and I bet she would have done the same thing on a machine of that size, or at least tried to anyway. She was probably a bit stronger than the girl mentioned here though. The point is, she was not scared or timid. I was down at Land between the Lakes in Kentucky several years ago and a girl about 11 or 12 was riding a KFX 700. She was the daughter of one of my coworkers. She seemed to be handling it pretty well and she was simply average size for her age. That's a quad I would have to have some respect for as an adult or I would get hurt myself. Its a machine that will run 70 mph. I kinda cringed when I saw a girl that size on the KFX 700 as it did dwarf her.

 

Is bigger better? I find myself riding my Mid chassis 350 more than my full size chassis 500 lately.
It's easier to hop on and off of and much more manverabe on our tight twisty trails.

 

In this case, a mid size 350 would be bigger than the youth quad she has now. I think the real question is does she even need that? A full size 500cc machine is way too much for a novice rider like this. Too inexperienced and not big and strong enough to handle it. The logical next step up would be a Honda 250ex or Suzuki Z250 sport quad. They are 2wd sport quads with semi-auto foot shift but are both on the smaller side compared to any 4x4 quad. The utility versions of both, the Honda Recon and Suzuki Ozark, might actually be better choices. Both offer a bit more legroom, full floorboards as opposed to just footpegs, bigger fenders, and more low end torque for trail riding. They even have racks that you can actually use and a little more ground clearance too. No 4wd but putting more aggressive rear tires than stock on them will get you through a lot. Cost is pretty low too, can find a Recon or Ozark in good shape in the $1500 range used. The Recon can be found with the optional electric shift (ES) where you push a button on the left handlebar instead of using your foot to shift. For someone who has only rode cvt auto quads, this would most likely be easier to master.