Tracking models showed Irma will make landfall on the Keys and head along Florida's west coast, bringing 120 miles per hour wind gusts to the state that is a major tourism hub, with an economy that comprises about 5 percent of USA gross domestic product.
'We allow those animals to decide where they want to go, ' Mr Dowling said.
Irma, which has killed at least 22 people in the Caribbean, was likely to inflict billions of dollars in damage in the third largest US state by population.
More than 4.4 million customers of the state's two largest utilities may lose power, according to company forecasts Saturday.
The governor also warned of the potential for hurricane-force winds extending north into the Florida panhandle, and said tornadoes are possible in south Florida this evening and central Florida on Sunday.
About 1.3 million homes and businesses lost power in Florida as Hurricane Irma pummeled the southern part of the state, Florida Power & Light said on Sunday.
What is happening in Florida?
BBC reports that the western Gulf coast is expected to be the worst affected because of Hurricane Irma.
The Florida Keys have suffered some minor damage and are expected to bear the brunt of the storm in the coming hours.
"This is a worst case scenario for Monroe County, the Florida Keys and the west coast of Florida", Brock Long, administrator of the Federal Emergency Management Agency, told the "Fox News Sunday" programme.
The Miami-Dade Police Department also said Sunday morning that its officers can not respond to emergency calls and warned residents to stay indoors.
Tens of thousands of people huddling in shelters watched for updates as the storm swung to the west, now potentially sparing Tampa as well Miami the catastrophic head-on blow forecasters had been warning about for days.
Rob Miller, a meteorologist at AccuWeather Inc.in State College, Pennsylvania, said a track "near or just to the west is nearly, if not, a worst-case scenario for Tampa Bay", said "It shoves all the water into Tampa Bay and then shoves it right into downtown". A major round of evacuations was ordered in the Tampa area, and shelters there soon began filling up.
The Pasco County Sheriff's Office warned that shooting weapons at the most unsafe Atlantic hurricane to hit the USA since records began "will have very risky side effects".
India, he said, over the last few years, have mounted to evacuate Indians and people of Indian-origin from various parts of the world - Iraq, Libya, Yemen and Syria.
Which other areas have already been hit?France's government is sending hundreds more soldiers and police to restore order to the Caribbean island of St. Martin amid looting and chaos after Hurricane Irma.
Barbuda: The small island is said to be "barely habitable", with 95 percent of the buildings damaged.
Puerto Rico: More than 6000 residents of the USA territory are in shelters and many more without power.
In a welcome reprieve for the Caribbean, a second monster storm, Hurricane Jose - which had been heading toward the same string of islands pummeled by Irma - began to gradually weaken and shift course towards the north.
Terrified Cubans who rode out Irma in coastal towns - after it made landfall Friday as a maximum-strength Category 5 storm on the Camaguey archipelago - reported "deafening" winds, uprooted trees and power lines, and blown rooftops.
In Key West, Carol Walterson Stroud and her family are huddled in a third floor apartment at a senior center.