You can paint over wallpaper - we had to do that when we moved into our current house - the prior owner had put the wallpaper directly on the drywall.
First, clean it as much as possible to remove grease, dirt, etc. Remove any loose paper, although you may be able to re-glue them in order to keep a consistent pattern, since you've stated you don't mind the pattern :)
Next, paint over with with an oil-based sealer/primer - there are some primers "designed" for painting over wallpaper, but the key is "sealer". You may need two coats of this, depending on the texture and/or color of the wallpaper.
Now, you can fill in any imperfections, and mud over the texture if you really wanted to get rid of it. You can even sand down any overlapping seams to make them less noticeable. Prime over any sanded or filled spots.
Now you're ready for paint. Finally, if you want to hide the spot and provide some defense from the next time, you can purchase plastic protectors that stick to the wall, and will prevent the door handle from making another hole.