It looks beautiful from the doorway.
The problem is the carpet is cool toned and the floor and banisters are warm toned. BUT the lovely stained glass window in the door has both cool toned brown and warm amber tones. I think once you have put up pictures, added a rug, furniture, plants etc and have a mixture of warm and cool tones it will bring everything together and the clash won't matter. Currently the effect is very harsh as all you have is 2 large areas that clash.
I would do nothing until you have decided on everything else. If it still isn't working, I would probably change the colour of the wooden floor and banisters, rather than the carpet, to a cooler tone. You could probably do it with a tinted varnish top coat, you don't have to restain them.
The black painted banisters are quite harsh but they do echo the black leading of the stained glass. Again, see how they work once everything else is in place. Retaping the carpet in black could help to tie everything in but it would be a bold look. You could get some cheap black ribbon and lay it on top to test out how it would look.
I would also consider the changing the white walls to a colour or a cream. That would help in several ways. The colour (or contrast if you go for cream) will draw your eye from the clashing warm and cool neutrals of the wood and carpet. It will balance out the mix of warm and cool tones. Also, it spoils the proportions of the original design if you have the same colour above and below the picture rail, and the original features just fade into the background if the plaster work and wood are all white too.
Don't rush though. Add the things that you were going to add anyway before you start making major changes. It has the potential to be stunning.