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As long as the weather is in your favor, I think you're set up to be alright. Oakville to NOLA is pushing the limits of what can be done safely in two days, but with 2.5 you'll be in good shape.

There's nothing wrong with leaving early, but I would caution against overdoing it. The last thing you want to do is to hit the road when everyone is tired and cranky from not getting enough sleep, especially since getting a family of 5 on the road is going to take some time by itself. Also don't think that if you get on the road at 5am, that you can drive until 10 at night. If you get on the road early, then also stop early to relax and rest up for the next day.

For a route, after Detroit, I'd recommend I-75/I-71/I-65/I-20/I-59 through Cincinnati, Louisville, Nashville, and Birmingham. I'd plan to stop in Louisville the first night, and I'd actually stop a bit short of NOLA, probably in Hattiesburg the second. As it is, those drives will already take 10-12 hours, especially considering time to cross the border. If you really want to make sure you spend the night in New Orleans, then you need to look at spending the night in Elizabethtown, KY, or Bowling Green - but that should be the absolute max you look to do in a single day.

Speaking of border crossings, if you've got a smartphone, try to get an update on border crossing times when you get around London, as it could be faster/easier to cross at Sarnia.

Of course, the other big thing you'll have to keep any eye on is the weather. If there is bad weather in the forecast, I'd see about even trying to get out on the road the evening of the 18th to give you even more cushion since you're on a hard deadline. You will have to look at the forecast across nearly your entire trip, as ice storms could potentially be an issue all the way into Tennessee and Mississippi.