This lady has her head on straight, that's for sure. She's "thin and straight as a nail, but she was kind." (4.28) As soon as Lina explains to her that Granny's not able to take care of Poppy, Mrs. Murdo agrees to look in on them several times a day while Lina's at work.
Pretty soon, Mrs. Murdo is taking care of Lina, Poppy, and Granny on a regular basis. And boy, does she do a good job of it: "She made sure they all ate a good breakfast in the morning […] She lined up the vitamin pills by each person's plate and made sure they were swallowed. When Mrs. Murdo was there, shoes got picked up and put away, spills were wiped off the furniture, and Poppy always had on clean clothes" (5.5). You know how much effort goes into keeping a house clean when there's a toddler around? Here's a hint: a ton. Mrs. Murdo is on top of her game, that's for sure.
In addition to being practical, Mrs. Murdo is modest. When Lina tries to thank Mrs. Murdo for taking in her and Poppy after Granny's death, Mrs. Murdo doesn't seem to want to hear it:
"It's lovely," Lina said. "You're so kind, Mrs. Murdo."
"Well," said Mrs. Murdo briskly, "It's just common sense. You need a place. I have one. You go on now, and I'll see you this evening." (11.13-14)
Mrs. Murdo is kind and selfless. She does what's right for common-sense purposes. And that means she's a good lady to have around in a jam.
Funny thing about Mrs. Murdo? There's no Mr. Murdo that we see in the book. No kids, either. We're thinking she's probably widowed, like a lot of the adult characters seem to be. This doesn't lead us to think happy thoughts about the life expectancy in Ember.
It's unfortunate that Mrs. Murdo was alone before Lina and Poppy came into her life, since she is really caring when you get down to it. During the blackout that happens after the Singing, Lina knows that Mrs. Murdo has "her arms wrapped tightly around Poppy, trying to protect her" (16.52). She truly cares for the girls, which is touching.
After they disappear, we see a brief glimpse of Mrs. Murdo, "walking even more briskly than usual to keep her spirits up" (20.67). We get the impression that she misses the girls a lot, and is concerned for their safety. But then, that means she'll be receptive to the message that Lina and Doon toss into Ember from above, containing instructions on how to exit the city. Hopefully Mrs. Murdo will act on those instructions, so this new-ish family can be reunited.