They didn't let the dove out, it just was there already. 'Twas a symbol. Besides, birds weren't stored inside the Ark, they could fly and rest on high-elevated land. :o
They tried a duck first but it never came back 
The Unicorn was actually the first. Noah quickly realized it couldn't swim. Luckily, it could fly. So it flew away, hoping to report Noah to PETA for throwing it in the water. c