360 miles in a day is doable, but unless you average 65mph, you won't make it in 6 hours, it will take 6.5 to 7 hours. You'll stop for fuel, lunch, potty break, slow down for intersections, on / off ramps, traffic, weather etc.
Sometimes we'll make 450+ miles I a day, but I don't like several days in a row of it. If you have three weeks, it sounds like you're still working and on vacation time. If so, then you do what you have to do.
If you're not on vacation time, then get off of the freeway and take some of the back roads and see the smaller towns.
Since it will be a several day drive, you might consider setting your schedule so that you don't arrive at your destination after dark. It's always easier to get situated and set up during mid day.
Bill