I don't see why one would display in one window and not the other, however, go to ALT+O > IRC and under 'Show in active', check the box 'Whois'.
"whois whois $$1" isn't going to work, as it will attempt to /whois the user 'whois'. I guess you mean /whois $$1 $$1.
Anyway, with the aforementioned box checked it works for me.
Regards,