Shoe moulding along the base moulding (since no more carpet) and a threshold in front of the door (you can rip a 1x2 or 1x3 with 22 degree bevel... or buy a door threshold and rip in half, flush to the bottom under door). I would stain/finish to match the wood and not paint it.

You can either use construction adhesive under the threshold, along with finish nails (set and putty the holes) or drill holes for recessed screw and glue a plug over, sand, finish.

Sry if too much suggested. I did this to a room that I removed carpet and the doorway was a bit higher (previous owner chiseled out the threshold. Nice oak hardwood flooring under carpet was the reward..but had to have pro finisher for floors...) Oh, if you do shoe all around, get primed-jointed pine, and paint before installing. Then its just putty nail holes, caulk, and touch up.