Joe Jonas is back on daddy duty ... it's his turn to look after his two kids as his child custody agreement with Sophie Turner moves forward.

The Jo Bros singer spent part of his Friday running errands in NYC with their daughters -- 1-year-old Delphine and 3-year-old Willa -- carrying one kiddo in his arms and getting her squared away in her car seat.

Joe's got the kids through November 2 under the terms of the temporary child custody agreement he and his estranged wife hammered out earlier this month.

TMZ broke the story ... Joe and Sophie are close to signing a settlement in their divorce, and child custody has been the biggest sticking point.

While Joe literally has his hands full with the girls, Sophie is back in London ... filming the final scenes for her TV show, "Joan."

Sophie handed the kids off to Joe last weekend -- she had them from Oct. 9 through Oct. 21  before passing the baton off to Dad.

Once Joe's time ends next week, Sophie gets the girls until Nov. 22 ... and the calendar seems to line up for Joe to spend Thanksgiving with his kids.

Makes sense, Turkey Day's big in America, and not in Sophie's native United Kingdom.

Remember ... Joe and Sophie hashed out child custody issues earlier this month during mediation, and it looks like the plan is working so far.