OP only wants a range of 1 metre, so power will be so low it would be difficult to triangulate him!
Don't underestimate a simple oscillator. The Michigan Mighty Mite that I have posted a link to is a single transistor affair, producing about 500mW of power at 12V. If you happen to connect that to a piece of long wire that will act as an antenna, you can achieve transcontinental contacts with it. It has been done. Even with a much poorer antenna you will easily cause interference - the fact that your primitive receiver is unable to pick the signals up at more than 1m doesn't mean that someone else with a better equipment can't.
Unless you are planning to only ever transmit into a dummy load, you should assume that someone may (and will) hear your signal.
Did you have a particular frequency in mind? There are a few license exempt bands available.
Most license-exempt bands, such as the various ISM ones or the CB band don't really allow homebrew equipment - the equipment needs to be certified and not user-modifiable (=tamper-evident seals, fixed power limiters etc.) to be able to operate there legally. Not something an amateur is likely going to do.
Also, with the exception of CB, most of those are in the upper VHF and UHF, (100MHz+) ranges - not something easily approachable for a beginner wanting to build something from scratch, not using a pre-made module.
Pretty much the only bands where you can meaningfully and legally experiment with transmitters are HAM HF and VHF/UHF ones - and for those you do need a license. The exact laws and rules differ between countries, of course - e.g. the popular wireless "bugs" or microphones that one can receive on a normal FM radio are illegal in the most of Europe but supposedly OK in the US (different max. power limits).
If the OP is interested in transmitters and radio (it is a wonderful hobby, btw!), I strongly suggest he gets at least a basic HAM radio operator license. Most countries don't require Morse code anymore, the exam is often only a test from the rules and basic operating skills.