My first comment would be to avoid the DIY sheds for this sort of thing.
I idly Googled solid door knobs and came across World of Brass, that operates a website. The point about chromium plating, if that is what you really want, it is invariably on a substrate of solid brass, or at least a brass-plated base metal, onto which the top chromium plating will stick. This organisation does more than supply brass items.
Another organisation that I have used before is Ironmongery Direct, and I found them good.
You get what you pay for and a solid item is likely to cost around £50.
If all that sounds too much trouble, look in local press for a small plating company on the local industrial park who may be able to plate your existing quality brass plated item, though it might cost around £50 also as a small one off batch.
What I wouldn't do is try to paint it yourself. Hard to make it look right on such a visible item of door furniture.