The pair died after a tree fell on their home Friday, according to a tweet from Wilmington Police. The child's injured father was taken to hospital.
Some 11,000 power outages have been reported in North Carolina.
In North and SC was energized more than 620 thousand households.
The extremely unsafe hurricane has already caused more than 500,000 power outages and more is expected in the coming days.
More than 60 people had to be pulled from a collapsing motel at the height of the storm, CBS Greenville affiliate WNCT-TV reports.
"WE ARE COMING TO GET YOU", the city of New Bern tweeted around 2 a.m. "Nothing you need to get a chain saw after yet", he said by phone.
Florence flattened trees, crumbled roads and knocked out power to more than 700,000 homes and businesses, and the assault wasn't near an end.
Storm surges, punishing winds and rain are turning some towns into rushing rivers - and the storm is expected to crawl over parts of the Carolinas into the weekend, pounding some of the same areas over and over. It was crawling west-southwest at 3 miles per hour (6kph), lifting huge amounts of ocean moisture and dumping it far from the coast.
The sixth Florence related death is also the first reported in South Carolina, according to both the South Carolina Highway Patrol and the Union County Coroner's Office.
Florence "is twice the size of Hurricane Hugo", which tore through the Carolinas in 1989, New Bern Mayor Dana Outlaw told "GMA". "It's an uninvited brute who doesn't want to leave".
Governor Cooper said the hurricane was likely to "continue its violent grind across the state for days".
The weather event has been downgraded from a hurricane to a tropical storm but forecasters still warn of life-threatening storm surges.
It was expected to begin pushing its way westward across SC later in the day, in a watery siege that could go on all weekend.
Preparing for the worst, about 9,700 National Guard troops and civilians were deployed with high-water vehicles, helicopters and boats that could be used to pluck people from the floodwaters.
Whether residents left their homes, sought refuge in a shelter or are hunkering down, the weather service has bad news: After creeping inland, Florence "is expected to slow down even more today and tonight". At 5:30 a.m. a reporter in a downtown hotel here in Wilmington heard the signature hurricane sound - a low, heavy humming combined with an nearly musical high note.
Florence remains a Category 1 storm, and it's spinning hurricane-force winds up to 35 miles from its center. In addition to the 20,000 evacuees in North Carolina shelters, SC housed 5,500 people in 59 shelters as of Thursday night, a state Red Cross spokesperson said.
Authorities in New Bern, a town of about 30,000 people that dates to the early 18th century, said more than 100 people had to be saved from floods and that the downtown area was underwater.
Donald Trump was to visit hurricane-hit zones "early to the middle of next week", the White House said, "once it is determined his travel will not disrupt any rescue or recovery efforts".
The NHC said hurricane-force winds extended outward 80 miles from the center of the storm and tropical storm-force winds extended almost 195 miles out.
In Bayboro, North Carolina, one of the areas under evacuation, resident Kim Dunn stayed behind.
Saturday night, state and county officials confirmed more deaths, including three people in Duplin County, who died in floodwaters.