According to regulations, all animals may be transported in wooden cages – dogs, cats, ferrets, rabbits, birds, etc. In practice, however, it's much easier to send pets in travel cages with a hard plastic shell*, as wooden transport crates are mainly used when the animal's size doesn't allow for use of a plastic cage.
Wooden crates must be made to size, and are strictly required to meet the regulations in force. In addition, they are subject to the prior approval of the airline company. To do this, it is essential to have plans for the travel cage approved by the airline company before it is made.
*some modifications may be made, depending on the animal (the addition of a perch for birds, for example)