Wood has, historically, been used, and still is, to make a great variety of things. Indeed, this material has many qualities, the most relevant being:
Commonplace: in most places in your typical fantasy setting, you never have to go very far to find trees.
Easy to harvest and work with: chopping a tree down only requires simple tools and relatively little time and labor. It's also rather easy to cut, shape and assemble.
Strong and light: it's neither brittle nor malleable, and a relatively thin plank or pole is able to hold its own weight and then some.
Comes in long, slender pieces: this make it especially great for building free-standing structures.
Now, consider dwarves. A material with such qualities would be very useful to them. But dwarves live underground, and trees don't grow underground.
So what materials, that are readily available underground, could dwarves use in place of wood? There are obvious candidates, but they are either too heavy and hard to work with (stone), to fragile for most uses (clay), or require lots of infrastructure and labor to make (metal)...
So would a dwarven kingdom need to regularly send lumberjacks out on the surface, or be reliant on wood imports? Or are there alternatives?
For reference, here are some things I think dwarves would need wood for:
Scaffolding to temporarily support construction or provide access to elevated areas.
Crude fortifications (palisades) that can be erected quickly and with minimal dwarfpower.
Crates to store goods and materials, and carts to transport them.
Doors and (movable) furniture such as tables, chairs, benches, etc.