The main problem is that you can't dungeon queue with your chocobo out. Personally I'd do the daily dungeon queue while bashing out crafting dailies or gathering for the GC provisioning missions, and hopefully by then the queue will have popped and you can just solo grind fates with your chocobo buddy to heal you.

From 30 or so you can probably start leeching off of other people's fate parties in Coerthas, and it's mostly smooth sailing from there, it's just the levels from 15 to 30 that drag a bit.