The state so far has been spared from severe hurricane impacts, but the southwest portion of the state is expecting up to 12 inches of rain.
Officials said the father of the child was injured in the incident; he was taken to an area hospital, the New Hanover Regional Medical Center.
"It's the first time we've ever had to move anything like this", Rose said.
SC recorded its first death from the storm, with officials saying a 61-year-old woman was killed when her auto hit a tree that had fallen across a highway. Florence is moving slowly across eastern SC, and according to the National Hurricane Center is producing "catastrophic flooding over North and SC".
The storm originally made landfall at Wrightsville Beach, North Carolina, on Friday as a category one hurricane.
"It's the worst feeling in the world to hear people yelling for help, and you can't do anything", she said.
On the other side of the world, meanwhile, more than a dozen people have died as Typhoon Mangkhut rips through the Philippines. A husband and wife died in a house fire linked to the storm, officials said, and an 81-year-old man died after falling and hitting his head while packing to evacuate.
There were 974,000 homes in the Carolinas without power on Saturday morning.
Risky storm surges and rising tides have caused coastal areas to be flooded, with water rushing inland from the shoreline.
The National Weather Service is forecasting the river to crest at Manchester at 35.4 feet at about 8 a.m. Monday.
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Nearly 800,000 people are reported to be without power in North Carolina and officials have warned that restoring electricity could take days or even weeks.
Holt, who has diabetes and clogged arteries, said she stayed for doctor's appointments that were canceled at the last minute.
North Carolina utilities estimated that as many as 2.5 million state residents could be left without power, the state's Department of Public Safety said.
Authorities ordered the immediate evacuation of up to 7,500 people living within a mile (1.6 kilometers) of a stretch of the Cape Fear River and the Little River, about 100 miles (160 kilometers) from the North Carolina coast. As we get closer toward the middle of next week, Florence's remnants should be near or spreading across our area.
The deaths bring the death toll from Florence, which came ashore on Friday as a hurricane, to at least seven.
Near the flooded-out town of New Bern, where about 455 people had to be rescued from the swirling flood waters, water completely surrounded churches, businesses and homes.
A man who was trapped inside his New Bern, North Carolina, home by Tropical Storm Florence spoke with Fox & Friends on Saturday.
The city of about 29,000, which was founded in the early 1700s and was briefly the state capital, is near the North Carolina coast and is bordered on the east and south, respectively, by two rivers.
Florence is expected to unload a total of 10 trillion gallons of rain on North Carolina, weather.us meteorologist Ryan Maue said.
There have been "several hundred" rescue operations, Governor Cooper said.
The president may travel to the region next week, the White House has said.