I took my daughter to WDW in May when she was 12 weeks old, and again in June at 15 weeks, and we just got back from DL last week and she's now 6 months old. My advice would be to stay home!!!! Like others said, you never know what will happen. My daughter came 2 weeks early with an easy labor, so I thought an easy delivery would follow, but I was wrong. It wasn't that bad, but 2 hours of pushing and almost 2 hours of stitching up the internal cuts and tears the forceps damaged nerves in my out thighs/knees, causing them to be numb. I had this numbness in my legs for over 6 weeks after my daughter was born (actually, I still do, but it's not as bad and going away slowly) and at 4 weeks it was pretty bad, at times causing me to misstep and misjudge the strength of my legs/knees. At 3 weeks postpartum I went to a neurologist who told me it was the result of keeping my legs in that 'pushing' position for almost 4 hours, and pressure from the baby's head on a specific nerve that damaged it and that in time it would hopefully regrow. Like I said, I'm still waiting. Other than the numbness, I had so much pain from the internal stitches (and I thought not needing an episiotomy would save me from stitches) that sitting without the 'donut' was near impossible for 4 weeks. I felt better walking, but boy did I pay for it later when I sat down with intense pain and pressure inmy whole pelvic region. Also, someone mentioned age, and I was 23 when my daughter was born and everyone says it's easier to heal when you're younger (obviously I can't compare).
Aside from issues with your own well-being, you might get a challenging baby. My daughter was not able to be put down for the first 3 months of her life. Well, she was, but she'd scream until she was picked up again, including sleeping. While this was exhausting, at least at home I had the swing, my husband, vibrating pack n' play to give me a short break. On vacation I would not have had these items, and if I stayed in the room alone with her all day (especially with limited tv channels) I would have gone crazy. When she was 3 months we actually brought her aquarium travel swing with us so that I could do things like shower, but what a pain to lug that along. Also, partly because my husband is a medical student and therefore paranoid about illness, but also because of her ped's recommendation, I wouldn't have exposed her to such large crowds at that age, not to mention the heat in WDW in June. May wasn't that bad, but when we came back in June (we were there May 19-25 and June 7-21) it was unbearable. People warned us but we thought "it's only 2 weeks from now, how different can it be!?" But wow was it hot and humid. My daughter was drenched in sweat everyday and she hates to be hot/in the heat so time spent outdoors wasn't her favorite. She was cooler when I carried her in the Baby Bjorn rather than in her stroller, but then I was incredibly hot, which I dealt with since she was happier that way. Actually, my daughter hated her stroller at that age anyway and only wanted to be held, even more so at a month. Yours might not be like that, but you never know, and previous kids aren't the best indicator as my niece was a 'perfect' baby, but her brother was just like my daughter. My daughter's 'high-needs' really exhausted me and I would not have been able to handle a family vacation at that age.
Last week in DL we had a great time. She loved all the characters and loved looking around on all the rides and shows she was able to do. She's still very needy, but at least she was able to sit in her stroller and play in the pack n' play for short periods of time, so it was easier to be away from home. We're planning to go back to WDW in April when she'll be 14 months (hopefully this December too when she'll be almost 10 months).
I wouldn't hesitate to take my next baby at 6 months, or maybe even 3 months again, but not a one month and not if it is in the summer. I know you said your older kids would be upset if you cancelled the trip, but you did say you have a few other trips planned, so I'm sure they'd be fine with you moving the trip. Since you can't cancel at the last minute, I would reschedule now either for before the baby's born, or when it's a little older. It'll be easier on the whole family and you'll have a much greater trip. You'll be able to join the rest of your family in the parks and you won't have to worry about the baby being in the sun or with large crowds, etc.
