One of the common woods used for carving and for dollhouse and other scale-model applications is called basswood, which is commonly available from hobby and model shops.
You can use many other woods if they are close-grained enough, including proper furniture woods like maple, but they are much harder and more difficult to cut and the may be difficult to acquire in small pieces or useful profiles/sections.
Any wood can actually be shaped by knife, this is what whittling is all about*, but, you won't easily cut wood down to size and shape it fully using a knife alone.
Saws are vitally important for some aspects of woodworking, regardless of the scale of the work, and while you can split wood along the grain fairly easily cross-cutting is one thing where there is nearly no other option but to use a saw. Using just a knife you can't cut wood across the grain in a reasonable amount of time, especially where accuracy and neatness in the finished item are important.
So you do want a saw (or saws) for at least some of the work. In the case of dollhouse furniture you won't generally use full-sized hand saws, instead for model work there is a lot of use made of smaller saws and very fine saws such as razor saws.
I'd also say that files of various types should be high on your to-get list, above sandpaper and other sanding equipment in fact (although you will need some of that too). I'd get at least one set of needle files, which should have a fairly standard selection including a triangular file, a couple of flats of various shapes, possibly a square, a half-round and a round or rat-tail file, all of which will prove very useful for some of the shaping you'll need to do.
See some previous Q&As for more info that might be of help:
Comparison of Western saws and Japanese Saws
How do I sharpen curved tools like gouges?
How can I tell if wood turning (lathe) chisels are sharp?
*Note that whatever type of knife you use it should be kept as sharp as possible, sharp enough to shave arm hair is the minimum standard to aim for.