If you have the diode, capacitor etc wired correctly as a diode probe, you should be able to measure the RF voltage without any problem, and from there calculate the power. W = V*V/R.
However, there are several "traps".
The voltage measured by the diode probe will be the peak voltage rather than the RMS voltage needed fro the avove calculation.
Vrms = Vpeak/1.414, for a sine wave.
The impedance of your dipole is almost certainly not what you expect!
Try using a dummy load.
The antenna is at best 1 metre away from your multimeter, (you state that the transmitter connects to the antenna via 1 metre of coax).
RF from the antenna will get into you multimeter, especially if it is digital, and cause it to read any old rubbish, which is what is happening to you.
This is a very good example of poor EMC, (Electro Magnetic Compatibility).
Moving the antenna away from your tx and meter, or using a dummy load should clear this situation.
As Nigel said, I hope you have an amateur radio licence for this lot.
Jim GM3ZMA