The rate of oxidation is going to depend on a few things. Beer tends to get oxidized when it's splashed or agitated in the presence of air. This can also happen if the beer is in the presence of pressurized air, rather than pressurized CO2. If beer is just sitting, like in a secondary fermenter, it could probably sit, undisturbed, for a few months with no oxidation. Even in beer that is seemingly done fermenting, like in a secondary fermenter, there will be a thin layer of CO2 across the surface from the last gasps of fermentation or off gassing of the very small amount of CO2 dissolved in the beer. If undisturbed, this thin layer of CO2 will protect the beer from being oxidized.
What is your situation? What kind of container are you planning to store in? How long are you planning to store?
As with most problems in brewing, I would look first to sanitation. Review your sanitation procedures. Make sure that everything that touches the wort once you turn your burner off is sanitized. Also, I would look into a wort chiller to speed up your chilling process.
You do not have an oxidation problem. Oxidation usually takes a bit of time to develop and probably wouldn't be noticeable in the secondary fermenter.