First, you wrote this function:
uploadtime[filesize_, bandwidth_] := (filesize/bandwidth);
You can use this function with Quantities. For example,
uploadtime[
Quantity[12770776, "Bytes"],
Quantity[2.4, "Megabits"/"Seconds"]]
Quantity[42.5693, "Seconds"]
As you can see, there is no need to call UnitConvert. The division operation handles unit conversion automatically.
You mentioned that you also evaluated:
UnitConvert["Month", "Second"]
Quantity[2628000, "Seconds"]
Is this correct?
Can you type-out what calculation seems to not be working for you?