Microamp-milliamp Measuring Circuit: will my circuit work? Feedback/Advice
It all depends on the specs (range, resolution, accuracy and speed) you set for yourself.
The 1uA to 10mA range is a relatively large range. If you want 1uA resolution, then you need 10'000 A/D steps which would mean you need a 14 bit A/D converter.  If 10uA resolution is fine with you, then you have 1000 A/D steps which can be done with a 10 bit A/D converter.
There's a simple trick you could do: You could use 2 different shunt resistors in parallel for two different current ranges (low/high). Then you could dynamically switch one or the other shunt resistor into the current measurement loop by means of some transistors. This way you could go with a simple 8 bit A/D converter.