It's a common mistake to assume this should be capitalized because it's a proper noun. Like most questions of this type, the answer is that grammarians don't agree on a definite rule, and that context may dictate each instance.
In general, references to breeds should not be capitalized unless they are part of the formal breed name. There are two major exceptions where Poodle would need to be capitalized--if someone was talking about an actual dog or if someone was writing something referencing mythology by referring to the famous three-headed watchdog Cerberus from Greek Mythology who resembles a poodle in many ways...