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Per Google and a non-functioning website, this appears to be closed.

Lots of room for walking a dog, including a walk with a few exhibits and historic signs. No dogs areallowed in the two hangars with the main exhibits. The museum is great, so you may want to plan around this if going with your dog.
Note the large main parking lot is uphill from the main buildings. There are also a few spaces by Hangar 1, accessible from a different road entrance.
Regional note: If planning to include a visit to Tuskegee University, only service animals are allowed on campus - no other animals at all.

Lovely gardens and trails to walk your leashed dog. We saw only two other dogs on a weekday visit. Note that there is an entrance fee.