This can be a tricky scenario. If your daughter was not on your policy, you would not have to worry about a rate increase because you were the not-at-fault individual. However, because she is on your policy, filing a claim would impact the rate of the entire policy. In Illinois
in 2017, an at-fault accident raised rates from $1,120 to $1,588 - to about $468.00 per year. Consider, as well, that an at-fault accident will stay on your record for 3 years. If she were to move out and get her own policy, the accident would follow her and your rate would return to around what it was before. I would consider the $2,000 versus the $468 (over 3 years, so $1,404 plus whatever your deductible is) and see which financial burden is easier to deal with. If you'd like some more information on the claims process, check out our handy guide: How to File a Car Insurance Claim: Steps, Timing, and Costs to Expect
If you do file a claim, remember to shop around with other insurance companies. The amount you will be charged for an at-fault accident will vary greatly between car insurance companies. Use our comparison calculator here
to see what other companies might charge you.