Your niece would likely be covered by your car insurance policy if she were in an accident in your vehicle, but it ultimately depends upon the terms of your specific personal auto insurance policy.
Many car insurance policy terms will cover permissive drivers, which is generally defined as individuals who live outside your household and whom you allow to drive your vehicle. However, some auto policies don’t cover permissive drivers; thus, it’s important to read over your policy terms and even call your insurer to verify your coverage before allowing anyone to borrow your vehicle who isn’t listed as a driver.
Besides checking that your auto policy covers permissive drivers, also make sure it doesn’t contain step-down provisions that would lower your limits, or exclusions for drivers under a certain age. (See “You might have less car insurance than you think”)
Then there is also the issue of how much your niece will drive your vehicle. If she is going to start driving it on a regular basis, then you should inform your car insurance provider to see if she has to be added as an occasional driver to your policy. Rules for occasional drivers vary by insurer, but some say it is someone who operates your vehicle more than once a week on a consistent basis.
If you have to add your niece to your car insurance policy, it could affect your car insurance rates. If it makes a negative impact on your annual premiums, but you want her to have use of the vehicle, then compare car insurance quotes to see if you can get cheaper rates elsewhere.