Possible Clues:

• One might fake its death
• Australian marsupial (which Americans begin with an 'O')
• Critter that might play dead
• Animal that plays dead
• Pogo, e.g
• Marsupial that can take an O at the start
• Marsupial so quiet climbing on the whole?
• Marsupial seen in North America
• Marsupial, familiarly
• Australian arboreal marsupial, also called a phalanger