The problem with that circuit is that it's going to splatter all over the shortwave band - an RF signal needs to be spectrally pure within legal limits, and within bands you are legally entitled to use.
That circuit produces a square wave, not a sine wave.
You can get various legal and cheap modules for the unlicensed ISM bands, from simple wire-replacement tx/rx pairs to packet transceiver modules and all the way up to mesh network nodes like the Xbee's
Be aware that if your circuit transmits over a sensitive frequency such as fire and rescue services or aircraft bands you run a risk of endagering other's life and safety.
Also an effective aerial for 1MHz is awkwardly large anyway.
Can I use the same circuitry as in the above link, and just change the code to "receiving code"? Im not sure what it would have to do, but i am imagining something like another interupt timer, also set to 1Mhz listening to data coming in on an analog pin - or maybe continuous listening, because the two devices might be completely out of sync.