I just tested posting the JSON to this app:

import vibe.d;

static this()
{
	void handle(HttpServerRequest req, HttpServerResponse res)
	{
		static int cnt;
		res.writeBody(to!string(cnt++)~"\n"~req.json.toString()~"\n", "text/plain");
	}

	auto settings = new HttpServerSettings;
	settings.port = 8080;
	listenHttp(settings, &handle);
}

and the response is instantaneous. Is there anything else happening in your app? If not, does this simple app also show the delay for you?