-- Q: --
Isn't the world going to be totally collapsed after the Rapture?-- A: --
When all the Christians on the planet disappear, there will certainly be massive confusion.**********
However, the majority of people will still be on earth, and communications will be their first priority to maintain.
Therefore, I believe it will not be a problem to coordinate activities to rescue and care for your pets.
UPDATE: Apocalypse Not
"By late afternoon, a small crowd had gathered in front of Camping's Oakland headquarters. There were atheists blowing up balloons in human form, which were released into the sky just after 6 p.m. in a mockery of the rapture."
"Someone played a CD of 'The End' by the Doors, amid much laughter."