You can't repair the veneer, of course. You could use a patching compound to flatten the area and then touch up with black, semi-gloss. However, that will only lessen the apparent damage, not hide it.

If it were me, I'd consider cutting a strip of oak the same dimensions as the top and about 1/2" thick, giving it a bevel edge, finishing it with a black, semi gloss spray paint, and gluing it over the damage. That way it would look like an intentional design detail, rather than a patch. If you don't have the capability to do that, I'm afraid I don't have any suggestions that are easier.

In any case, be glad you didn't have a fire.

I'd make a shelf, about 3 to 4" wide and as long as the headboard is wide, and affix it to the top.
If you don't want a shelf, you can get iron-on oak veneer edging at home depot, etal, to resurface the headboard top.

If I were to patch it, would you recommend a grain filler or wood filler (or something else)?

A grain filler is intended to fill the tiny pores of grain to smooth out a finish on an intact, solid wood surface, so that's not what you want since you've got deep damage that goes down to the particle board. Try a quality wood filler (not a wood putty) like Elmer's or Minwax brand. Use a filler that's water-based, not solvent-based, as it will be easier to smooth out and cleanup where the patch meets the undamaged edges before the material sets up. (Also, a solvent-based filler could damage the existing finish.) Use a couple inch wide joint compound knife to spread it evenly; it may take more than one application because there is sometimes a little shrinkage. In order to get it perfectly flush with the adjacent surface, you may need to carefully sand it with a small sanding block. Good luck.

Thanks everybody for the helpful information! Is DAP 'plastic wood' water or solvent based? Also, any suggestions on a grit# for the sandpaper?

Any 'plastic wood' product is going to look pretty bad, even after you try and paint it.

Using some oak veneer and cutting it in as a 'Dutchman' then staining and finishing to match can make an almost invisible repair if done carefully.

Any filler material is NOT going to have the correct texture and make (at best) a smooth spot that will be readily apparent.

ljbrandt- DAP Plastic Wood is solvent based. If you see solvents listed on the label, it's solvent based. A fine sandpaper -- 180 to 240 grit or so -- should work.

brickeyee- I agree that there are better ways to do this...but I'm getting the sense that the OP doesn't have the tools and skills to do that.

"I agree that there are better ways to do this...but I'm getting the sense that the OP doesn't have the tools and skills to do that."

They are most likely going to make it look worse, and not be very happy with the result.

brickeyee - any suggestion on where I can find suitable oak veneer? Would a hobby shop possibly have the veneer and stain (and finisher?). I'm going to have to google dutchman cut. Thank you!

"any suggestion on where I can find suitable oak veneer?"

Constantine's should have everything you would need,

Tools, stain (dye) and finishes.

Here is a link that might be useful: Constantine's

ljbrandt-
So, tell us how this all turns out when you are done. Good luck.

will do, ill post pics after im done

Do a search on 'Dutchman' and there are multiple sites with instructions.

It is not that hard, but getting a tight fit can take a few tries.