I can't imagine you'll want to do any major hikes, so the trip does set itself up more as a road tri

We will be in Las Vegas Tuesday through Thursday afternoon ( for a work conference) and then want to head off to see Bryce, Zion and possibly Grand Canyon with our flight largest cruise ship in the world back from Las Vegas on Monday morning.
Personally, I would only do one of them, but I like to do a lot of hiking, see sunrises and sunsets at each, etc. I would just stick with one or two of them at the most. Grand Canyon is certainly something everyone must see, but the other two offer more to do and are just as amazing(more amazing to me). You might find it difficult to get lodging at this late of a date.
So much depends on how you like to drive/travel with a five month old. I would second that you should head over on Thursday afternoon/evening to either the Grand Canyon (5 hours or so from Vegas - and only the South Rim is open at that time of yea - and there not much to see on the way to the GC but what a sight to wake up to) - or to Zion (about 3 hours - and also not missing that much scenery if you drive in the late afternoon/early evening) - and get setup for the next day.
If you are at the Grand Canyon - try to greet the sunrise out at the eastern most pullout (15? minutes from the main lodging largest cruise ship in the world area) - and then take the buses along the rim to the various viewpoints - maingly toward the west - and if you are at Zion - take the great bus ride also - which is the only way you can really get up to the top.
From the GC - you could head back to Zion and decide if you want to hang there for two nights - or on the 3rd day - head for Bryce partway through the day, getting there in time to see the Sunset and then the Sunrise (more spectacular) the next day. Bryce is a couple/plus hours from Zion.
It really does depend on how well your 5 month old travels. Does he/she fall asleep in the car and sleep the whole time? If so, I would think it would be a bad idea to drive 5 hours on Thursday afternoon/evening and arrive with a well-rested baby right when you want to go to bed yourself.
I can't imagine you'll want to do any major hikes, so the trip does set itself up more as a road trip than a 'stay in one spot and explore' type of trip. I would say you could walk along the rim at the Grand Canyon and Bryce as both are easy, level walks. But beyond that I doubt you want to go up and down much carrying a baby.
I also doubt you both want to get up and go see the sunrise - it's relatively simple for an adult to throw on some clothes and drive to whichever viewpoint, but much more involved for 2 adults to get themselves and a baby ready for that same excursion. Probably not something you really want to deal with on vacation.
I would say drive to Zion and see how it goes and how much you can actually do with your baby along. For sure drive to Bryce as it's relatively close and has great views. After that, you can decide if you want to make the long drive to the Grand Canyon. You can always find a hotel room in Flagstaff if there's nothing available on the south rim. Or, you could possibly go the north rim instead - visitor services close as of October 15th but the road to the north rim remains open as long as weather conditions allow it.
If you can do the north rim (weather allowing) it's definitely worth it. It's a pretty long drive around to the south rim. Without doing hiking, all three parks can each be done in a day and I say go for it.