Until I provided her with the manuals of why not, my wife was keen on trying this with the Cathay crew for baby milk... 9 times out of ten it's a no (unfortunately for me, that one time was the first time...).

If you ask nicely then the FAs will provide you with ice however on boarding or through the flight, so bring a cool bag/container and bag for the ice and since it's a short trip it will be fine.

Note this is normal ice, I can't imagine anyone can give you dry ice on a plane?