It doesn't quite match yours, but here's one from Van Dyke's.

And here's another from Constantine's:

http://www.constantines.com/toilettepinantiquebrass.aspx

Don't throw away the old hardware if you replace it! Keep it with the mirror.

Your mirror is late Victorian, probably 1880s, in a style sometimes called ball-and-spindle. It looks like it's either walnut or mahogany.

Here is a link that might be useful: Mirror supports from Van Dyke's