I'm due with my 2nd baby about a week before you (8/28) and my dr plans to induce at 38 weeks also (cause my dr was born 15 days early and 8.4 lbs) and I had the same thought about planning a trip 9/30 to take advantage of the
free dining! My end decision is that we won't be going (well, unless something can change my mind) but it was a hard thing to decide on. If my son does end up coming at 38 weeks he'd be around 7 weeks or so by 9/30, but I just keep thinking "what if he comes closer to his due date? what if he has medical problems? how will I manage with a 2.5yo who wants to see everything now and a newborn? what if I'm still not feeling up to full days at WDW?" With my daughter I had a decent labor/delivery, but lots of internal stitches from the forceps, double mastitis, and nerve damage to both legs causing me to be numb from the hip-knee for 6 months after she was born. But with all that, by 6 weeks old I was at a bridal shower and felt totally fine.
We took my daughter for her 1st trip at 1 week shy of 3 months old and I will admit it was the easiest trip we've ever taken with her. BUT she was my only child and we were with extended family and friends (the trip was planning before the baby was). This time I will also have a 2.5yo so even though the baby may be easy, I still have another kid to contend with, who will inevitably get hot, tired, grouchy, etc. Not sure if I can handle that while being hot and tired myself, plus caring for a newborn. Also, I breastfed my daughter so I didn't have to take bottles around with me, but what if this one isn't such a good nurser? Then I've got more gear to tote around.
But, the positive for you is that you would drive (we'd have to fly) so that would make it a bit easier, IMO. And your 1st child is older than mine also making it a little easier. If we had extended family to go on this trip too then I'd probably end up going this fall, so maybe if you have someone you can tote along that would be a good option. Oh, and yes, it's hot, but it was hot in May when we took my daughter and she was totally fine, never overheated or dehydrated, and she didn't cry once the whole trip (and this was a very, very high maintenence baby at home for the 1st 4 months). One last thing, my husband will be a dr as of 5/21 (and is the biggest germophobe you'll ever meet as a result) but he really didn't have any qualms about taking our daughter so young and didn't mind the thought of our son going even younger. And this is a guy who wouldn't let anyone other than our moms visit the hospital or house when she was born and made everyone who touched her wash their hands before every touch till she was 4 months old. Maybe cause we live in a city and walk most places so WDW wouldn't be so different.
So I wouldn't say don't go, just giving my reasons for my very hard decision being in almost the same situation as you.