Prior to the 4-legged wonder we have now we nurtured a 3-legged dog from losing her right front leg at 3 months to just shy of 15 years.  For her I got carpet with a 1-inch foam pad (the pad was super cushy and was 25% the cost per square foot as the carpet...it was all for her).   It was an awesome decision for her. 

Lucky for you the loss of a rear-leg is much less impactful in terms of walking/running across hard surfaces.  Most of a dogs weight is on the front legs.  So I think she can manage the hard wood without a problem once she recovers. In fact if the throw rugs are sliding they may be doing more harm than good.  I used to walk in the park occasionally with another owner with a young dog that lost its rear leg in a car accident and she never had to consider impact damage to her dogs feet/legs.  I was constantly managing split pads, swollen shoulders etc from the pounding my dog's front leg took.  I would watch the dogs missing a back leg and be jealous. They could walk or run and turn left and right more easily as their front wheel drive was intact.  Missing a front-leg my dog had a very hard time walking slowly and pretty much could only run in a straight line or make a very wide turn.

Because I was so sensitive to padding on the floor for my 3-legged pup I insisted my partner put some carpet with backing on his hard laminate foor in some areas.  Any carpet store usually has the option of selling a carpet to a specific size and making it a rug by stitching the edges and sewing on a backing that makes it non-slip. They are basically custom sized rugs that don't slip.  Our 4-legged dog will run through the house by leaping from these sections of carpet to stay on the padding as much as possible.  All dogs, 3-legged or not, love soft surfaces so having some is a good idea.