Well, with bitcoin-qt, you can't really send a zero-fee tx unless it is a high-priority one.
You will need to play with raw tx
But, you can create a zero-fee tx very easily with Electrum
as I remember in december 2013 I was sending transaction from Bitcoin-qt with 0 fee.
I sent 0.0001 BTC to try how long does it take to trasfer.
Hmm it is going to be hard to find tx, because I had so many wallets ...
I haven't got qt installed, I can't give it a try
I might be wrong about this.