Switching current source ~1 μA — how to switch off quickly?
You could use a PNP differential pair that always stays active.  Drive the bases to either shunt the current to the load, or to ground.  That should provide very fast switching of the current, although the current is always flowing somewhere.  This is similar to how ECL logic circuits worked, and why they are able to get high switching speed.

There is some good information on differential pairs here: http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/part1/page3.html