Ketchum, ID. is at 5,800 ft. altitude. Jackson, WY. is 6,200 ft. altitude. The pass is 8,400 ft. Altitude. There are twists and turns. Roads tend to go around mountains instead of over them out west. I've driven it in a 'C' pulling a Jeep, but its been too long ago to remember details.
You certainly want to drive through the parks, assuming you will have a National Parks pass. If you don't, get one. It will save you money.
Even though YNP and GTNP are next to each other, they're different. Be sure to drive your toad to the top of signal mountain in the Tetons. There's a viewing platform at the top and you can see several states from there. There's a map at the top so you'll know what you're looking at. Don't try to walk up unless you enjoy pain. Very steep.
Suggestion: Use the two letter state designations. There are four states with a "Ketchum". Twenty states with a "Jackson".