We live in NJ too and have driven with our kids since our oldest was 5 weeks old (and she is now 17). My family doesn't like to fly so driving is normally our choice and we actually like it. Depending on where in NJ you're starting from, investigate both 95 and 81 (which you could pick up either in PA or you could take 95 down to the Beltway, then go west and pick it up in VA). 81 is a longer route but we like it better (not as crazy, a prettier drive, just less stressful). A few tips from our experience over the years...we have what we call the "toy bag" which is a duffel of travel-friendly toys that they can only play with on drives. The toys have evolved over the years, but I can tell you that's one thing my kids love, seeing what's new in the toy bag. We rely heavily on movies (get a portable DVD player if you don't have one in the car) and books on tape. When the girls were younger we would do a lot of car bingo, I Spy, Going on a Picnic, etc. We share the driving and go for about two to three hours before we stop for everyone to use the bathroom, grab a snack, top off the gas, etc. The girls bring their pillows, a blanket, their phones, books, anything that will make them happy and comfortable on the drive. When we were younger we would go straight through, but now we tend to stop in Savannah or northern Florida (we try to not be more than about three to four hours out from Disney when we stop). If we're taking 95, we leave NJ at either 2:00 am or 5:00 am but not between, as leaving between 2 and 5 would put us at the Beltway at rush hour and you just don't want that. If we're taking 81, we go west on the PA Turnpike and we try to leave by 2:00 am because the 81 route adds a couple of hours overall to the trip. As others mentioned, watch the weather and the traffic and make judgments based on them. We like Waze for traffic and Accuweather for weather.
As others also mentioned, what's really going to make a difference is how you and your daughter handle a long car ride. My kids have grown up with it so it's no big deal for them, but if anyone gets antsy after a couple of hours in the car then this is not your way to travel. Try a couple of day tris and see how everyone does and then make a decision.
Also consider the Auto Train. You pick it up in Lorton, VA, just south of the Beltway, and it takes you overnight to Sanford, FL, which is about 45 minutes from Disney. You can get a room (which we have done and I definitely recommend), and the ride is comfortable. You could also take it just one direction if you wanted.
The drive is definitely doable, but just like if you were driving, you need to prep for it and go into it with the expectation that there may be delays, accidents, etc. But it can be really fun too.