Road Trip from Vegas to the National parks in Arizona and Utah

Given your very limited time I'd skip Bryce and spend that extra time in Zion.  While you still won't get the full Zion experience, even just doing full drive through the park will be a very memorable experience.  Definitely follow the advice from others about booking slot canyon tour ahead of time but no matter what do the slot canyon - its one of our favorite road trip experiences.  The walk from the parking lot to horshoe bend is long, hot and up hill so bring more water than you think you'll need and take frequent rests.  Enjoy - these are all amazing places.

Also, since you asked for suggestions for a better plan here's mine: Start your trip the night before you planned – drive the 3 hours to Zion and spend the night. Wake up early… like at or before sunrise… and do as much as you can in Zion for the day. You could hike the Angel's Landing trail (start early, it gets crowded – allow 3 hours) and explore other areas of interest in the park. Skip Bryce – save it for another visit when you have more time. From Zion it's a 2.5 hour drive to Page so you could have an early dinner at the lodge and still make it Page by 10 pm.
Sunrise at Horseshoe Bend would also be lovely and you'll avoid the heavy crowds that show up later in the day. Aim for a late morning (no later than noon) tour of Antelope Canyon – the light is best that time of day. You'll still have a long drive to Phoenix, but day 1 will offer you more outdoor adventure with less time behind the wheel.

If all you want is to snap a selfie for Instagram and to claim the bragging rights for having been there, then sure, it's doable. But it's hardly enough time to see much of anything or to appreciate where you've been. Leaving Vegas at 9 will get you to Zion around noon. You'll have time for a short hike, maybe some snapshots at some overlooks, then leave at 2 pm to arrive at Bryce by 3:30. It's a 30 minute drive to Rainbow Point, so you'll spend an hour driving inside the park. No hikes here, just gazing at the view from the car, jumping out quick to snap some selfies. 5:30 you're on the road again for a 3-hour drive to Page. Scarf down some fast food, check into your motel and flop exhausted on the bed by 10 pm.
Luckily both Horseshoe Bend and Antelope Canyon are right near Page. A 15-minute drive and 30-minute hike will get you to the overlook at Horseshoe Bend. 10 minutes for selfies, then hoof it on back to the car and drive 20 minutes to Antelope Canyon. Hope you booked your tour in advance because they often sell out, and you must arrive 1.5 hours before your entry time to check in for the (typically) 2-hour tour. By the time you're done, it's 2 pm. Now you can drive 4.5 hours straight to Phoenix or half that to reach Flagstaff, then 2.25 hours the next morning to Sky Harbor International Airport (give or take with traffic). Hope you enjoyed your 48-hour 730-mile trek through the desert.