The frets are actually replaceable parts made from fretwire. They are sunk into slits in the fretboard wood. Ask your local guitar shop to remove the frets, or try for yourself using a pair of pliers. You can somewhat protect the fretboard by taping it during removal.
After that, you are left with a slitted fretboard. From a woodworking aspect, I would fill the slits with a wood putty, and carefully levelling the result (maybe sanding). But I would not expect the result to be perfect, because the putty will be of different hardness than the wood.
If the finish is no good, the fretboard too can be replaced, but I dont know how that works. Unslotted Fretboards are available in shops.
Fretwire looks like this: http://www.stewmac.com/shop/Fretting_supplies/Stewart-MacDonald_Fretwire.html
Unfretted fretboard looks like this: http://www.stewmac.com/shop/Bodies,_necks,_wood/Acoustic_guitar_fingerboards/Unslotted_Fingerboard_for_Guitar.html