There are several different places to get power for your switch and light. You need to find something that is hot all the time as opposed to switched.
SOME ceiling lights have hot power in them (as opposed to switched power) . The easiest way to determine this is to remove a switch from the wall. If there are only two wires in the sw box (black and white) there will be power in the ceiling box.
If the light box in the other room only has black and whtie then you can't use it for power for your new light unless you want the new light contolled by the switch for the first light.
You need to find a source of unswitched power like a receptacle to power you new fixture.