This is Rainbow Bridge.....
http://www.petloss.com/poems/maingrp/rainbowb.htm
that binky behaviour , my daughters called it " flicky 10 mins " so it stuck
what do you call it when they throw them selves on their side for a 5 min nap, we called it " doing a flopsy" our rabbit did it so hard his legs ended up pointing skywards and ended up in his hypnotic state for 5 mins