Welcome to the Apple Community.
You can mirror your desktop, if your computer meets the specifications.
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).
no you will not be able to mirror out of the box
the mirror rely on the video card of the macbook being able to convert the signal on the fly
and only the newer models support that
you can try the software called airparrot it does the same thing but without using the video card but the main cpu so the performance is likely not to be as good