Broken fork and front wheel after head-on crash, need to replace headset?
I am sorry to hear about the crash!

You do want to get a bike store to inspect the bike. Headsets can take damage in crashes like that, but we don't know for sure. If the headset was damaged, how it happened was probably that the fork steerer banged against one of the races and dented it, which would cause your fork to feel loose in the headset and not turn smoothly. Ride like that, and over time, I think you have a good chance of damaging the head tube.

As @nollak and @DanielRHicks mentioned, you also want to make sure that your frame is in alignment (and this is not something most people have the tools for at home). Guys, your comments could have been answers.