I see no issues with taking the route you have planned. It's very doable in a RV. You'll have Powder River Pass to cross so you'll have a climb from Buffalo and a descent to Worland. By the time you get from Florida to Wyoming you'll be an old hand at driving these roads. You'll also have some of it in Yellowstone itself so this will be good practice. :) Just know how to brake your RV correctly. Downshift before you even start going down not when you're midway. It's short and it'll soon be over! We've done it often with our 40' motorhome and many RVers do it.
We would not do Hwys 14/14A.
I think the others are guessing you want to drive Hwy 14 and 14A. Your plan doesn't include that stretch.
This is the route you want:
From Buffalo take 16 to Worland and north to Greybull and west to Cody.
If you want to explore on Hwy 14 or 14A, stay in Greybull and take your vehicle.
https://www.wyomingtourism.org/things-to-do/detail/Cloud-Peak-Skyway-Scenic-Byway/7344
