Without standard solutions and a fluorimeter, you can do a side-by-side comparison using a commercial tonic water and your solution. I just prevailed in getting a poor photograph of the beautiful blue fluorescence from a commercial tonic water (begins with an S), using 405 nm excitation (BluRay laser diode). The photo is below:
The two cuvettes contain tonic water (undiluted on the right) and diluted about 5 times (on the left). The laser entered from the right. The bubbles must be removed because they cause significant light scatter that gives red artifacts in the camera. By naked eye, it actually looks lots better: no red artifacts.
Removing the dissolved gas, to avoid bubble formation, is often done done by using an ultrasonic bath, sparging or by simply shaking the bottle repeatedly and waiting. Adding NaCl is a no-go because it quenches quinine fluorescence (a nice Stern-Volmer experiment).
Fluorescence is very sensitive, but the standard joke is that only 10% of all substances fluoresce ... and they are the wrong 10%. But this is a good case!
So, you would simply A-B the solutions: make dilutions of the commercial tonic water and see which one most closely matches your home-made tonic water. Cheers!
Note: you can use near-UV LEDs, i.e., 395 or so nm peak emission wavelength. The absorption max for quinine sulfate in dilute sulfuric acid is around 350 nm, and the peak emission wavelength is around 460 nm. But the photo shows that 405 nm works fine: it is not always necessary to be at the optimum excitation wavelength. Driving an LED is trivially simple: just a DC voltage supply, such as a battery or 'wall wart', and a current limiting resistor. Or use a constant current source that can output 20 or so mA.
One more thing: if you dilute the tonic water sufficiently, you will not be able to see the fluorescence with the naked eye. But a fluorimeter can detect it at even lower concentrations. Eventually, with sufficient dilution, you reach the limit of detection. But that is way below whatever you might want in usable tonic water.