I think you need to decide exactly what you mean by quality and also understand that it constantly changes.
The only really accurate measure is unfortunately historical - i.e. you can do a download or upload test and measure the time it took and any packet loss, jitter, delay etc and this will let you know what the quality was when your test was run.
The reason I say it is historical is that this does not guarantee that it will stay like this for any given time - for example you may move between cells (or rooms in the case of WiFi), or several other users in your area may start utilizing the bandwidth heavily.
It may be that a simple download or upload test is sufficient for your purposes to (I am guessing...) decide if your want to run your application in a certain way, and then you can build in further checks into the application itself to see if you need to adapt to a change in the network (e.g. you could trigger on the time for a particular application message transaction to complete)