portable power supply
I think this means it uses 36 Watts per hour or 3000 mAh.


It means it uses 36 Watts, period.  In an hour it'll use 3000mAh, yes -- but a mAh is a measure of charge (one mAh is 3.6 Coloumbs, if you want to be irritatingly correct), not power.  

The light will probably work fine if you just connect it to a sealed lead-acid cell.  The voltage it gets will only be nominally 12V (it'll range from 13.5 down to 12 as the battery discharges), but that will probably be OK.

Battery capacity is rated ambitiously -- if you fully drain a battery you significantly decrease it's lifetime.  Get a sealed lead-acid that's advertised as having a capacity about 150% more than your calculation.  Then make sure you're charging it with a good charger (I'd use a model airplane charger that has a lead-acid mode -- the Great Planes Triton should be good enough).

My suggested capacity gets you around 22 pounds of battery -- that may be more than she wants to lug around.