Wood is actually a fairly flat texture to do, the reason is is that unless it has a rich stain the grain wont show up. Darken the lines for individual boards will also help add more too it. The texture you have there now is actually pretty good, I think those lines are all you really need.
Overall the shape is good, but it's VERY hard to make out the handle, try adding in a dark gray to the lower right of it, that'll give it a bit of pop since it'll contrast much more against the bright tope color.
As suggested remove the outline or make it match more into the overall theme for the icon, if you want a more realistic outline, then use a darker version of your current door color. By darker I mean about 2 shades. Clean up the lighting and pick a true lightsource.
Last piece of advice I can give you is.. just practice some more, find areas that don't look right to you and work on them.