Hi Brian, implementing this as part of a Mendix application is probably difficult. You could try to use the microflow timer widget and configure it to trigger on page load only, but it will probably fire before the page is fully loaded. There's also the mx.addOnLoad() function from the Client API, but I think it is also triggered too early.
At Mendix world we showed our solution for test automation of Mendix applications. It will not only allow you to write automated tests, but also to measure timings. The scenario that you've described is exactly one of those that we want to support. Maybe this is an option for you.
You could also look at other tools that allow you to do the measurements from outside your application.