Simple Morse code transceiver circuit
Assuming you're in the US, the first place I'd look is the Radio Amateur's Handbook. It's available at any library and has exactly what you're looking for: basic radio theory and circuits for transmitters &amp; receivers from trivial to very complex.

If you have a ham license, you can build a simple CW transmitter that's nothing more than a gated sine wave oscillator on the 40M band (bear with me: my ham license (Advanced) expired over 15 years ago and I may get frequencies wrong). Since an 8" antenna is very short at this wavelength, you won't get much range, but a little 50mW transmitter may be enough. However, it's very easy to build a transmitter for this band (7 MHz) so it's a good place to start.

For a receiver, I'd suggest a simple direct conversion one. Adjusting the frequency of the local oscillator will change the audio frequency of the incoming CW signal just the way you want.

I can't attach circuits because I don't have any recent experience with simple circuits that I know will work. Again, I recommend the Handbook because it's an excellent reference.
I built exactly what I described above when I was in 11th grade (decades ago :-) and with much easier component availability these days, to say nothing of much improved performance, I expect this would be a nice weekend project for a hobby-level experimenter.

An alternative that doesn't require a license would be to pick up one each of the little 318/434 MHZ transmitter/receiver pairs such as this. You will need to build a little audio oscillator to connect to the digital output of the receiver, but circuits for 555 oscillators are all over the web.
These little boards are cheap and very easy to use. However, I don't think you'll get half a mile range from them.