I have no AirPlay icon in toolbar yet after purchasing and installing OS X Mountain Lion

Welcome to the Apple Community.

AirPlay Mirroring requires a second-generation Apple TV or later, OS X 10.8 or better and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). It also requires the computer to be using wi-fi.

I learned this the hard way, after upgrading to Mountain Lion I discovered that my MBP wasn't new enough to use the AirPlay Mirroring with my Apple TV. I've remedied this with a new MBP but I have to be honest I'm a little miffed that they excluded it from a 2009 MBP. I'd like to know what the technical reasons for leaving that feature out of that model were.

ML mirroring requires tech in the new chips for encoding video. The requirements (seen above) were put forth ahead of time.

http://en.wikipedia.org/wiki/Intel_Quick_Sync_Video

Another option. I have been using Air Parrot (airparrot.app) to mirror to a TV in my other room from my mid 2010 27" imac with great success. Love the app! Just as easy to use as mac mirroring. Just thought I would throw out as another option for mirroring. I didnt realize untill reading this tread that having an older machine would would stop or not let mac mirroring work. Just installed Mavericks and thought I would have mirroring now... I guess I will keep using my Air Parrot app.