^^ oh we did the show first & then the dinners were always too late for us but they were nice about it.

They can't go in the pools but there is splash pad and otherwise no issue for us.

Any other cruiseline hell no. Disney? They gear their travels to families and children of all ages. You'll be just fine.

It's not a nightmare on Disney. They're very well suited for kids (I don't think of a year-old kid as an infant). There's a nursery (with nighttime babysitting)-- you pay extra for it but it looks very nice. And every dining room is totally set up for kids. The rooms are set up with curtains in the middle so there's a separated area for them, and they have pack and plays. They also have activities just for little kids, like play areas and a dance party every morning.
BUT-- they wont be able to go into the pools, only the toddler swim areas. And those areas are filled with bigger kids running around. And if you can wait until that child is three, you get free child care on the ship and a lot more options.
I think they're free at that age so if it's a choice between going or staying home, I'd go. I've seen plenty of tiny kids on Disney cruises.

Considering a Disney Cruise with grandparents and elementary kids. I also have a 9m old. She will be 11-13 Months old depending on when we sail. She just started crawling and may or may not be walking.

Is it going to be a nightmare to be on a cruise ship with an infant?

One option is for DH to stay home with the baby and I go with the older 2 kids plus my parents.