I don't have a link to a schematic, but just thinking about this idea, it seems to me that it would be easy to build an AM transmitter as follows. First, build an oscillator using one of the many logic IC RC oscillator circuits. To get variable operation up to 1.5 MHz you would need to build this on a pcb protoboard not a solderless breadboard. You would use a potentiometer to vary the frequency. You need to use HC logic to get the high frequency of oscillation, don't use 74C or 4000 series.
The oscillator would run off of, say, 9 volts power supply (like a battery for example).
Next, you use a logic buffer IC as an output amplifier. For example, the 74HC240 might be a good choice. You can put more than one gate in parallel to get more output power. The power supply for this chip would not be run directly from the battery. Instead, it would be passed through the secondary winding of an audio transformer (something like 600 ohms to 8 ohms type, where the 8 ohm winding is the secondary). The primary side of the audio transformer would be driven by your transmit modulation audio. You would probably need an opamp to go between a microphone and this winding.
It will be necessary to put a series resistor between the oscillator output and the buffer input, since they are operating at different supply voltages. A 10K ohm would be OK I think.
The output of the 74HC240 gate(s) would then be passed through a low pass filter, with a configuration of series L, shunt C, series L, shunt C, then the antenna. This filter would smooth the waveform and so reduce the harmonics to an acceptable level. The values of L and C would be chosen to have a low pass cutoff frequency at 1.8 MHz.
Now, who wants to draw up the schematic for this?
I've seen this done for an HF transmitter in the ARRL Handbook, 2001 edition, page 17.96 showing the project for "an experimental 1/2 W CW transmitter". I'm adding the idea of high level AM modulation by simply modulating the DC power supply to the output amp using the transformer.