How can I determine existing well PSI / GPM for dedicated irrigation well
Try this:  


Install a pressure gauge, either temporarily on a tap that the pump runs, or by tapping a a pipe for the right thread and screwing it it.  (Usually 1/4" or 3/8" NTP thread.  Should work with shedule 40 pipe.
If you can run the pump without a zone running do so, and record the pressure.  DO NOT DO THIS IF IT IS A positive displacement (piston or  diaphragm) Centrifugal and jet pumps will tolerate this, but it's a waste of energy.
Turn on your smallest zone.  Record the pressure.
Manually turn on another zone.  REcord the new pressure.
Turn both off, and turn on your largest zone.  Record.


If your system is capable of running multiple zones at once this tells you that you have pump capacity to spare and you won't have to worry much.



If the pump is a surface mounted pump, read the model and serial number data off and do an internet search.  If it's a submersible pump this information is usually with the starter box which may be in the house, or on a pole nearby.



Individual sprinklers may have either a number or a capacity on them.  Some sprinker system can accept multiple nozzles that are colour coded.  Look up the manufacture and colour coding.  If you have a combo that translates to 40 gallon per hour and there are 15 of them, then that zone is using 40 * 15 = 600 gallon/hour or 10 gallons per minute.



Worst case:  Usually there is a valve box with all the valves in it.  If they were considerate, they left a stubbed off pipe just for this use with a threaded plug or cap.  Otherwise you may have to install one.  

You would also want some sort of fitting and a short length of large diameter hose (1.5" flat lay hose is cheap, and is sold by the foot at farm stores.)  

Hook it up and see how long it takes to fill up a known volume.  Garbage can works for this.