We've flown long distance with both girls starting when they were around 6-7 weeks, and YDD's first trip to WDW was when she was 3 months old. They did great! ODD flew and traveled internationally from about 6-7 weeks until she was 3 months because DH was traveling for work; we were in Europe and Brazil.
For the first trip to WDW, it was a breeze. I would definitely say to go! I'm not trying to be snarky to the people who are saying not to go, but - for us, with ODD, the fear of taking a trip with such a tiny baby was much much worse than actually doing it. We went to Europe and then Brazil, and the hardest part was getting her passport. We were mostly in hotels and it was nice not to have to clean up after myself all the time, not to have to figure out food shopping and cooking, etc. Our kids were EBF, so there was no need to pumps or bottles or anything else. We had to travel with ODD because my husband was traveling for work, and it would have been a lot easier to go with him than stay home (and it was a wonderful experience, overall). We realized, after having done it, that it's easier to travel with a newborn than a 1-5 yo. So we actually made it a point to travel more with YDD because it was a nice break and the baby is so portable.
OP, I would actually have more trepidation about driving 18 hours, since at that age you'd need to stop every 3 hours or so to nurse the baby and they poop a LOT (ODD was a once a week pooper then; YDD would poop at least 2-3x a day and usually once was a blowout. When we went to WDW we always brought and usually used the extra-set-in-case-of-blowout clothes.) Also, as 1st time parents, if you are driving you will probably bring too much gear, because you can. If you fly, you're limited in what you can bring and then you realize that you really don't need that much stuff with a baby. Seriously, it felt freeing to leave a lot of that behind when we traveled.
Having BTDT, and since you'd probably make a game time decision anyway, I think you have a solid plan in place and would really enjoy it!