Unfortunately it seems as though Google hasn’t seen fit to implement (or can’t implement) this feature for Gmail.
If there was some way to export what you are currently listening to to a link, or output the data to a text/html file, it may be possible (in a round-about way) to get it to display what you’re listening to or definitely at least provide a link to the text/html file in your away message, so if people were interested to see what you’ve been listening to they’d only have to click the link. They’d then be forwarded to the file’s content.
I’m not sure if iTunes has the capability to export currently playing items to txt files, but it might be worth looking into as a DIY solution when there’s no proper way to do it.