I was a little older when I was bitten but I also had no lasting psychological trauma and bounced back really well.
One of my best friends was bitten in the face when she was around your nieces age (she needed about 50 stitches) and she also has no trauma from it. Not to mention, she now makes a living as a model. I'm sure your niece will heal up perfectly!
I know these are just anecdotes but kids are really resilient! Still, lots of love to her and your family.