She reports that the effort to find them is complicated, and made all the more so by the unique circumstances surrounding each case.
The faces of some of the more than four thousand children who became separated from their families either in the storm, or during evacuations, have been shown on TV screens ever since.
Hundreds, at least, are thought to still be apart from their parents.
"It's unprecedented," says Ernie Allen, who runs the National Center for Missing and Exploited Children. "The shear scale of this, the numbers of people we're looking for and the time frame in which we're looking for them, is something we've never dealt with.
"We normally work cases in which children are taken as part of criminal activity."
But now, he has taken on the task of finding Katrina's kids.
Hundreds of volunteers, many of them retired law enforcement officials, are searching for evacuated children who by now are spread out in shelters all over the country.
"This is old-fashioned, gumshoe detective work," Allen says. "And the exciting thing about it is, there's a scoreboard. You know, you get to measure your impact in terms of real human lives and you get to do it on a daily basis. There is nothing better than that."
The score so far, Moriarty says: more than 1,200 children returned to their families, sometimes in dramatic fashion.
For instance, little Arnold Learson was sitting glumly in a Tennessee TV station, when his father suddenly walked into the studio.
And of the 165 faces of lost children shown on CBS News programs to date, 127 had been reconnected with their families as of Sunday morning.
But investigators at the Center for Missing Children fear that the latest hurricane, Rita, will not only add to the list of the missing, but complicate the current searches as well.
"Evacuees from Houston and across Texas are on the move again," notes Allen.
Still, points out Moriarty, there is hopeful news: While the official number of children reported as still missing is staggering, at nearly 3,000, the number of children truly lost is probably much, much lower.
Says Allen, "We're dealing less with traditional missing children and more with fractured families. …There are children who are with one parent, but the other parent doesn't know where they are or even if they're alive. There are children with a grandparent. …Many of these children are fine and being well cared for."
But there are also children, he says, with the wrong parent.
Asked if he has any idea of how many non-custodial parents have taken advantage of this to take a child they don't really have a legal right to, Allen said he doesn't but, "We had a few, and we suspect that there's some more."
There's one other statistic that worries Allen: In the wake of the storm, 4,500 registered sex offenders are also unaccounted for.
But, Moriarty says, the volunteer, seasoned investigators, who have seen it all, are giving it their all, for as long as it takes.
"Our commitment to these families," stresses Allen, "is that we will continue this work, we will not close a case, close a single file, until every child is found, or until we know with certainty what happened to the children and their families.
Editor's note: If you recognize any of the missing children whose pictures are shown on CBS News broadcasts, please call 1-800-THE-LOST, or log on to missingkids.com.