Q:

How did Murph know what happened to Dr Brand?

At the end of Interstellar, Murph tells Coop to

 go find Brand instead of staying to watch her die

and her closing monologue suggests she knows that Brand is

 setting up the colony on Edmunds' planet.

How did she know anything about Brand's whereabouts or survival?

A:

When Coop first arrives at the station, he asks about Murph, and the doctor says "She'll be here in a couple weeks." So at some point during those two weeks it's reasonable to speculate Coop had been interviewed/debriefed about his experiences, and Murph had learned what he said before they finally saw each other. If this is the case, she would know that Coop had helped Brand escape falling into Gargantua just before he fell in himself, and that she was headed for Edmunds' planet--as mentioned earlier after the disaster caused by Dr. Mann, they had been planning to do a gravitational slingshot around Gargantua in order to get there:

COOPER The navigation mainframe's destroyed and we don't have enough
  life support to make it back to Earth. But we might scrape to Edmunds'
  planet.
BRAND What about fuel?
COOPER Not enough. But I've got a plan — let Gargantua suck us right
  to her horizon — then a powered slingshot around to launch us at
  Edmunds.

So based on this, Murph could infer that Brand was on her way to Edmunds' planet, and perhaps had had enough time to get there (for some discussion of why Brand arriving at Edmunds' planet probably happened at roughly the same time Cooper arrived at the station, see this answer). And Murph's use of the word "maybe" in her comments suggests she was just making some reasoned speculations on what was going on with Brand at that moment, not that she knew for sure:

She's out there ... setting up camp...alone in a strange
  galaxy...maybe, right now, she's settling in for the long nap...by the
  light of our new sun...in our new home.

