I doubt you will get down to 1mA with such a circuit and such a small shunt resistor.
It's clearly not a bipolar current source (it's a simple current sink). I'm guessing you implied you want a bipolar source (and several here have understood so, probably because of your 'DC bias' remark) whereas I don't see it clearly stated in your post unless I missed something. With a 0-3.3V input sine signal, you'll just get a current sink between Imin (won't be 0, there will be a significant offset) and 3.3/Rshunt basically. That could be what you wanted after all. Unclear. Also, with 5V supply for your DUT, make sure you'll have enough headroom - we don't know anything about your DUT.
Also, paralleling transistors in this way won't work properly as explained above.
Obviously if you parallel several current sinks as OM2220 suggested, you'll have to set your shunt resistors appropriately since all the sinks will add to the overall sunk current. Also obviously, the errors will add up.
With such a wide current range, I suggest paralleling several current sinks as above, each with a different current range, and ideally controlled independently.
Why would a current sensor be simpler than a basic shunt resistor? And besides the DC offset, it probably has enough phase shift (I haven't read the DS enough to figure that out) to render it unsuitable here.