This is a relatively transparent scam that is pretty common on the Internet. Most times it's based out of Cameroon in East Africa.
The bottom line is that someone showed you a picture of a puppy (probably stolen off the Internet) and conned you into sending untraceable cash to them. There was no puppy and there is no airline demanding money. That's just the scammers trying to squeeze a few more dollars out of you.
Anytime someone you don't know asks you to send cash via Western Union or Moneygram, you are being scammed.