You can absolutely furnish a bedroom with the equipment you have assuming you're not trying g to do anything crazy.
I have a nice cabinet saw, 6" jointer, 13" planer, small drill press, small bandsaw, and a collection of smaller power tools like routers, palm Sanders, etc. Those basic tools cover all my needs I have some other "nice to have" equipment like dust collector, large compressor, spraying equipment but none of that is necessary.
I've been an avid woodworker for years and even when my collection of equipment was much more modest I made a ton of furniture. And not some cobbled shit but high quality solid wood furniture.
On the subject of true solid wood furniture I would advise you not to get hung up on that subject. The presumption that solid wood equal quality and veneer equals cheap is total nonsense. I spent most of my professional career in furniture manufacturing working g for manufacturers of some of the most expensive high end high quality furniture money can buy and I can tell you most of it is not solid wood. In fact, for some components, particle board and veneer is far superior to solid wood. And there is a difference between cheap particle board and high quality particle board. But I digress.
It takes a lot of knowledge about the behavior of solid wood to make true solid wood furniture. If you don't know what your doing the seasonal changes will result in all sorts of shrinking swelling and warping that can wreck your project. If you dont know the construction techniques to accomodate the behavior of solid wood you'll end up with dressers that have drawers swelled shut, joints cracking and failing, etc.
So my advise would be go for it. Make some furniture. Don't invest in any new equipment until a specific project requires it and there won't be many that require more capability than you have now. And lastly, rather than designing your work yourself, look for sources of detailed plans from reputable sources. If you do that you won't make the mistake of choosing the wrong techniques and joinery and your projects will last. And you'll learn a lot.