Go for it! :)
Yes Dotty, you can chalk paint a headboard! I have done several and I love every one of them! I did use wax over my chalk painted headboard in my room but you may want a more durable finish on the headboard--a clear poly finish would work well. I have noticed that on my husband's side of the bed the headboard has been distressed by him as he sleeps! I had painted over a headboard that was previously painted using a dark gray color and I can now see the white paint now underneath along the edges. I could distress the whole thing or just paint over it all again. For now I am just ignoring it! You can paint over chalk paint/wax once it has cured and this was painted several years ago. I did use a cheaper brand of chalk paint on this so perhaps that is part of the reason. Some chalk paints are more durable than others.
If fabric, don't forget to seal with clear wax. If plain timber with no carved details, you could use clear or antique wax on top to seal, but if it has carving on it, then the Antique wax will highlight that detail. Enjoy the project!
Here is a post I wrote on how to paint with chalk paint. https://lifeonsummerhill.com/how-to-paint-with-chalk-paint/
Here is how I chalk painted my headboard and I love the way it came out https://www.homeroad.net/2013/03/chalk-painted-bed-dresser-top.html