One company, Architecture for Dogs, has quite a few suggestions on the subject of DIY pet furniture. (Warning: this site has a noisy intro, so you may want to turn down the volume on your speakers.) The site showcases furniture designers who have each created a special project for their beloved pets.
Because of their short legs, it's hard for dachshunds to meet their masters' eyes. Also because of their short legs, it's hard for them to get up on chairs. Is there no good way to get closer to the eyes? Stairs? With those too-long bodies, they may throw out their backs. How about something like a folded slope? This works. Let's make it long enough so a person can lie down too. Sunbathing with your dachshund on the veranda is good. The area under the slope is like a burrow for small animals. They can train there, digging down there to catch their prey. If you connect several, they can go anywhere, and form any shape. Multiple stacks in an atrium space make a ramp for the dogs to go upstairs.
Mount Pug is a mesh-shaped "mountain" assembly of thin and long 600mm (plywood) pieces as "branches." By combining the unevenness of each branch to form hexagons and triangles, the "branches" begin to support each other like the cells of living creatures. The "mountain" can be assembled without nails or a bond. Pugs are clever and mischievous. They make full use of the mesh as a nest and plaything. Toys and snacks can also be hung on the mesh.
(Images: Architecture for Dogs)