Your dad's insurance should cover you for this; you can report yourself unless you don't know who the carrier is. Unless your dad has a bad claims history, this should not have a major effect on his rates. Good luck.
The author of this post is licensed to practice law in the District of Columbia, Maryland, and Virginia. This post is intended as general information only, and is not provided as legal advice in connection with any specific case, and does not create an attorney-client relationship.
I am not licensed in PA, and therefore, this reply addresses the subjects generally.
Generally, this would be deemed an "at fault" collision. Depending upon the underwriting guidelines of your insurer (the internal terms upon which a person is accepted and retained as an insured, and also dealing with calculation of premium), an $800 claim may or may not result in a premium increase at renewal.
The bigger issue that you should consider is that the other party may file a lawsuit against you to collect the damages; alternatively, if he/she has the damage repaired through his/her own insurance company, it may file a suit to collect back the payment (that process is called "subrogation"). If suit is filed, and the other party wins, you will likely also be responsible for the payment of his/her court costs, which will increase the total amount payable. Thereafter, if the judgment is not paid (typically, within 30 days), your license and tags may be subject to suspension for violation of PA's "Financial Responsibility Law". To get them back, you would have to pay the judgment plus various DMV fees. Overall, it may end up being much more costly for you than the original amount of damages.
Finally, if you did have liability insurance, one of the duties that your insurance company owes to you is the provision of a defense (if they think that there is a defense to either liability or damages). However, in order to take advantage of that right under the insurance policy, you are responsible for promptly reporting the collision to the insurer, and making sure that it gets all material, including the police report, damage estimates, letters, and suit papers, pertaining to the incident. You will generally also be responsible for cooperating with the insurer in any investigation and defense of the claim; at the least, this will likely include submitting to a written or recorded statement. As to the latter, just make sure that it is really your own insurance company seeking it, rather than the other party's insurer.
It is always better to be forthright in a situation like this. It may be the case that the other party will accept periodic payments of the damages over a reasonable span of time. You will want to consider something like that rather than hoping that the matter will just go away of its own accord.