As anal as they are in California... It is legal, with a license, to take Collered Dove with an air rifle 365 days a year, no limit.
I Imagine if Nebraska does have a season or a limit it may be for control purposes.
Collered Dove are fairly easy to knock down, maybe fragile is the word I'm thinking of. My son has taken them with a fairly low powered pellet pistol, I believe 3.5 jules. He thought he was doing a good thing trying to keep them from crapping all over Grandmas patio and Grandma. I explained to him that hunting anything without a license just isn't worth the consequences.