I've figured it out and I'm unsure who's at fault here. Khaled probably could shed some light on it.
I am a PC Gamer so I have a set of Creative USB Headphones (+Mic). The internal beep does not work when I have them set as my output device.
When I switch my output device to speakers the internal beep works fine.
I don't know if it's an issue with mIRC or the driver for the headset. As the headset seems to work fine for everything else.