First of all, congratulations!
Second, sorry this is probably a bit late, considering it's the middle of our crazy Arizona summers...... Hopefully this still helps you out in possible future scenarios.
Alright, so basically, a banana has a growth habit of creating the leaves/flowers inside the stalk sometimes weeks ahead of the time that they emerge. That's why when you cut a banana plant in half, you can see several leaves wrapped up preparing to emerge. So, the plant could have started forming the inflorescence some time before the weather got a bit cooler, and since it survived, and apparently kept growing at some rate, the flower is just now emerging.
Separating a pup at this time might cause a little bit of trouble, considering the stress it can put a plant under, especially in cool weather, but it should be fine as long as you keep it warm... and ALIVE.
The only other problem I can see at this point, really, is a lower number of fruits due to a much lower photosynthesis rate (thanks to the lack of viable leaves, and lower light levels), but for all I know, the plant could have been stockpiling nutrients and water for this purpose.
I'd just say be excited for possible future bananas, and to be sure to keep it alive!
