It'd be easy to pipe markdown's output to konqueror if konqueror would take input from a pipe… oh, but it doesn't. So this road goes over a temporary file with markdown's output.
Maybe there's some konqueror native way to get other input than from an URL I don't know of.
I think that Konqueror supports the data: scheme. You could theoretically try to use this to display arbitrary data (you would probably have to appropriately encode it first, but you just pass a data: URI with no need of any sort of temp file).
-- Philippe Mavridis