Welcome to Over50sForum! The site for people over 50 to chat, make friends, discuss, share, and generally be part of something that's fun and friendly :)
Possibly this is a reference to menstruation. ‘Time of the month’ does rather suggest this. But consider the date: 1988. Would Punch even in its later days have wanted to mention this subject, albeit indirectly? It could just have meant that she periodically turned into werewolf. The full moon seen through the window does rather support the werewolf theory.
The dinosaurs are facing extinction with the coming of an ice age and are just playing in the snow. I am now wondering if awareness of our present danger was already understood forty years ago? Is it just chance that this joke appeared then?