I don't know if there are other species of copperhead in FL, but in NC there is only one species of Copperhead, the Northern Copperhead, and the OP's picture is most definitely NOT of a Northern Copperhead. The Northern Copperhead ALWAYS (even as a juvenile) has bands that start on the side--not the top--of the snake and are wider on the sides than the top. It looks, as others have noted, like a rat snake to me.
Here is an excellent site that compares the Northern Copperhead to other--harmless--species:
http://fwie.fw.vt.edu/VHS/venomous-look-a-likes/copperhead-look-a-likes/copperhead.asp
I agree wholeheartedly that children come before snakes, but it makes me sad to see how many beneficial snakes are killed out of fear. Snakes are key predators of many creatures that are major human pests--especially rodents that can plague humans (quite literally--they carry many human diseases) and fowl alike. Yes, they eat eggs. But for every egg eaten by a snake, there are hundreds--probably thousands--of egg-eating rats and disease-carrying mice consumed by snakes.
I'm sure the snake didn't want to be in the house any more than you wanted it there. It was a mistake--it probably came in through an inviting-looking hole and got lost. My son once found a black rat snake under the recliner in the living room. I had a newborn at the time and no hands free to deal with it, so I had my compassionate neighbors come over and capture it in a sack and release it back in the yard by the wood pile. Thankfully, my neighbors feel the way I do about snakes and are grateful for them. The snake has never troubled us since.
All of that being said, I don't know offhand what kind of venomous snakes Florida has. So I googled, and it turns out they don't have the Northern Copperhead, but rather a similar species aptly called the Southern Copperhead. Apparently the Southern Copperhead is basically like the Northern except slightly paler. And only present in the panhandle. Apparently, there are no native copperheads--at all--elsewhere in the state of Florida.
Here's a link that shows the six venomous snake species native to Florida:
http://venomoussnakesfl.com/
I know killing the snake made sense at the time, and I don't blame you if you thought it might be venomous. But I hope at least some folks reading this will think twice before killing snakes they find, even in the home.