I've had a hard time finding active Corgi owners in Austin, but here are some general dog park events in Austin. We'd love to see other Austin area Corgis with their humans!
Dog Party organized by Yelp.com
This is an all-breed, all-sized-dog event starting with a hike at 11:30am at Bull Creek District Park and ending at Freddie's dog-friendly restaraunt.
(Charlie and I are not planning to attend this event, but check it out if you're looking for something to do Sunday. The weather should be great!)
Norwood Estate Dog Park, 1:00PM
I35 at Riverside Drive
This is a Small Dog Meetup group for dogs under 30 lbs. (If you have a 35 lb Corgi, I doubt anyone would complain.) We'll be in the fenced section of the park reserved for small dogs. This group plans to meet every 1st and 3rd Saturday.
(Charlie and I will be attending this meetup if the weather is nice.)