I just posted this for chickens, so ill post it here as well, same principal, just with your cat in a small room instead. [Disclaimer, i am not a professional dog trainer, have just spent much time around dogs, and successfully introduced hunting adult dogs to chickens and cats 3 times]
I dont know much on poodles, but sheep dogs are very good about recognizing the masters prey animals as things to protect. Some dogs, even within breeds, will require more or less training, so much is dependent on how your dog reacts and how well they learn. Just be to make sure the dog views you as master, this is important not matter what you are doing. Dogs need a clear leader, and if you dont provide that they will be more stressed and try to fill the role themselves, even though they dont knwo what they are doing. A masterless dog is miserable, but the occasional firm disciplinewill help them feel comfortablethey know what they are doing, and lead to a happy dog.
Some dogs will have no troubles, but i tend to have dogs with high hunting instincts. For chickens I would leash the dog very tightly and take it into the pen/close proximity. Let it sniff the birds, but if it snaps or try to chase sharply jerk back, give a swat on the nose, and if it doesn't settle then flip on the back and a light choke grip with shake [mostly digging fingers on either side of the windpipe, as another dog would to threaten, not actually chocking or blocking blood. Then hold the dog there until they stop resisting, take your hand away a bit and when they go to get up pin them again with a growl. Do this until they stay a momnt when you remove your hand, then give them permission and pat their belly. This is the most serious discipline you can give a dog, so dont over do it, but it is good at least once to show them you really mean it, you ARE in comand.] Repeat this for about 10 mins, 3-4 days in a row, as the dog is calmer around the birds encourage with pets and praise and a looser leash. If the dog shows no agression to the birds at all give a treat when you leave. After that bring the dog with on a loose leash every time you go out to them. After a week or 2 the dog will have learned and you can let them mingle without problem (mostly likely

). You may have to get onto the dog for excited chasing with no intent to kill a few times, so i would monitor for the first week of free mingling, but that should be it. Good luck!