You don't always have to sand like crazy when you use filler if you are going to paint afterwards, provided you apply the filler smoothly enough in the first place, usually using a nice wide scraper (may look a bit rustic in the end, but might be better than what you have now). In any event, if you want to do that, it will be easier to work on if you remove the back. You might also consider wallpapering the back (again, if possible, remove the back first to make the job much easier).

KarinL

Hopefully they meant past wood filler.
It is used to fill the grain of oak and other woods when a smooth surface is desired.

Behlen markets theirs as 'Por-o-pac.'
It is available in both solvent and water based.
The water base will of course cause some grain raising.

You thin the filer slightly (naphtha for the solvent base) and paint it on.
After it flashes off the naphtha it turns from glossy wet and you wipe off the excess across the grain.

Burlap works well, as do plastic putty knives.

If you are going to paint it should not need any sanding unless you do not remove enough.