Used to do claims and it depends on the amount of damage. If they replace the panel with a used or aftermarket one, it shouldn't be that much. If they repair it, it could actually more depending on the damage and labor time. Plus if the dent is bad, there will be lots of bondo.
Most shops will give you a free estimate. Get quotes at the dealer and also a reputable independent shop or two to see the difference.
Again, if you are paying out of pocket look for a used panel. If you live in a city, Hnda Civics are popular and a junk yard somewhere will have them. As a claims adjuster I had to push A/M, but not all parts are created equal. A used panel is the same as a new one though by the time they get done with it.
Overall I would be surprised if it more than 750-1,000 unless it's a lot more damge than you think. The front panels are tough becaue they have to remove and reinstall a lot of components and blend it with the rest of the car as best they can.