The inability to queue for DF with a chocobo summoned has been a problem for a while now. My guess is it has to do with how your chocobo is registered as being a party member rather than a pet like the Carbuncles or Fairies. When your party composition changes it pulls you out of DF and you cannot enter a duty with a chocobo so because it registers the chocobo as a party member it causes both things. Though I don't know much about coding, but this is just a logical guess on why it can't work currently and that I recall them saying it's been difficult to fix due to how it's coded. It's sorta become one of those up in the air things they've told us they're working on like official add on support and we really haven't heard much about for a while.