Airplay will work with your Macbook Pro. It works with my Late 2011 Macbook Pro. I used it Monday evening to watch the Apple Watch announcement on the 55" TV with my Wife.
When the Apple TV is turned on and talking to your home network, you will have an Airplay icon in your menu bar, and Apple TV will be an option in your System Preferences -> Displays
Also System Preferences -> Sound will have an option for where your sound goes when using Apple TV.
I think your Macbook Pro cannot be locked into using the integrated graphics processor. There are 3rd party utilities, such as gfxCardStatus that can do that, so if you are using one of those, then you need to switch to the Discrete logic graphic chip. NOTE: I am not 100% sure about the integrated vs discrete graphics chip, so take that with a grain of salt.
Apple TV turned on
Apple TV on your home network
Macbook Pro on your home network (NO VPN software running either)