I have never had an issue with a Doona on Delta, AA or United.
Add Southwest to that too. Not only no issue, the reaction you get from people who haven't seen the Doona is always fun.
The Doona is heavier than the Nuna, but you can push it all the way up to the seats, making it better than Nuna IMHO.
Refuah Shleima, and may your future travels only be for good.