Hi there John and Doug, yes my understanding is that for birds the paperwork gets more complicated. It is possible, there are people who have brought their birds down but you may find the extra requirements a bit time-consuming. For detailed current info it is best to ask a relocator or attorney that deals with this regularly, if you don’t have one try:
The Law Offices of Rainelda Mata-Kelly
Suite 406-407, Tower B, Torres de las Americas
Punta Pacifica, Panama City, Panama
Local tel: +(507) 216-9299
From the U.S. or Canada tel: (011 507) 380-0606.
E-mail: rmk@mata-kelly.com
Website: http://www.mata-kelly.com
For other animals like horses and cows yes, the process is more complex, Cats and dogs are the most common and thus the processes are the easiest/most streamlined.
Hope this helps.