Can anyone give me an idea of how to convert my mg/l Dissolved Oxygen in water to ppm?
Ppm is ambiguous as it can be a ratio by weight, volume, or mole fraction. Which do you want?
If ppm by weight is OK, a liter of (cool) water is pretty close to a kilogram (for high accuracy work, you could look up density as a function of temperature). Simplistically using 1 kg of water = 1 L, you would have mg/kg, which IS ppm by weight.
At 20 °C, density of water is 0.998 kg/L. If you really had the supporting accuracy in your O2 figure, you could divide by this as a minor correction. As water approaches normal boiling point, density is about 0.95 kg/L and correction should probably be made.