You can claim her as your dependent:

1. She meets the qualifying relative test as she is your niece.

2. She meets substantive presence test (residency test) as she has been here in the US for 183 days in the consecutive three years including the tax year (per your calculation)

3. You support her more than 50% (the burden of proof is yours in case of audit)

4. She has gross income less than $3,500 (for 2008)

5. She does not owe any tax to the IRS and she does not file the tax return on her own (even if she does it is only for tax refund purpose). 

I don't see any problem on your claiming her as your dependent. Again, in case of audit, the burden of proof (evidence) lies on you.