Pets are extensions of their owners' personalities, small
versions of their masters. Most people prefer pets with whom they can
innately relate, who reflect their own character traits, but it is
better to keep a pet who is therapeutic for your own imbalances.
Vatta people do well with dogs, for example, because a canine's
lovable, sloppy, openheartedness warms, reassures, relaxes and
stabilizes the Vattas cold, fearful, fickle nature. Kapha individuals
do better with small animals like birds because an avian's light,
bright cheerfulness helps offset some of a Kapha's natural
ponderousness, sluggishness and fixity.

Some Kapha people find large dogs beneficial because both dog
and owner need vigorous exercise, and responsibility for the canine
encourages the Kapha person to exercise along with the, dog. Some
Vatta types do well with small furry high-strung animals like guinea
pigs and hamsters, which elicit maternal instinct from their owners.

Pitta personalities are sometimes too overbearing to obtain much
incen-tive for self-development from the simpler personalities of
birds and beasts. Pittas should not take the easy way out and select
an animal who is too easy to get along with, nor one who is so
aggressive that the two beings feed off one another's instincts to
violence. A large long-lived bird like a parrot may be complex enough
to demand attention from a Pitta, but cats, who have strongly held
opinions about most subjects including their masters, present
continuous challenges to the probing Pitta mind and make perhaps the
best Pitta pets. The Pitta has to keep up with the feline, and this
is a refreshingly new experience for many hotshot Pittas.

From Prakruti by Robert Svoboda

For an intro to Ayurveda go to http://www.ayurveda.com/online%
20resource/intro_ayurveda.html