The first thing I'd like to address is the concern about your daughter's portion of the premium increasing. Since you are both covered on the same policy the overall premium is going to increase if a claim is filed. While you both impact the rate based on your individual rating factors like age and driving history, the accident is going to be filed under your name since you were the driver at the time of the accident. So technically any increase that you might experience because of the accident would be attributed to you and not your daughter. For example: if you both purchased separate policies in the next three years
, the accident is going to impact your rate and not hers since it will be filed under your name.
As for my recommendation, it's a good idea to first get a repair estimate for the damage before you make a final decision. If the repair cost is within reason for you to pay out of pocket then that will help you avoid any increase in your premium. If the repair cost is unaffordable for you to cover on your own then you really have no choice but to file a claim and pay the deductible.
Ultimately the decision to file a claim will be completely up to you, but paying for the repairs out of pocket means you won't have to involve your insurance company.