Welcome to RTA!
While most airlines will think twice before putting a family out because of children, it's better for the kids all round to be in a car anyway. At least, IMHO. My daughter and her husband decided to drive for much the same reason -- less expensive in the long run, you see more even through the windshield, you're not exposing your child to as many germs, and more.
How long are you planning for the trip? While this trip can conceivably be done in two very long days on the highway (taking I-5 the whole way), it would be better for all of you to do it in 3 days or even in 4 (one way). You'll want to stop every couple of hours and let your little one out of the torture chamber called a car seat, just to run. You don't have to stop anywhere fancy -- all s/he'll need is a place to run, whether it's at a rest area, city park, or state forest.
Stopping for gas - if the one who rides shotgun has a smart phone, get the Gas Buddy app (if you don't already have it). You might want to get gasoline when the price is "right", when you're down around a half tank. That's a good time for the non-fueler-up person to take the toddler out for a run. There are gas stations all the way up to Seattle, there's no place with more than 20 miles between stations that I know of.
Attractions -- and I mention these if you are taking 3-4 days to get up there: DO stop at the Shasta Overlook, nice viewpoint, good place to stretch your legs. Castle Crags State Park might be another place for a leg stretching. Over the Oregon border, is the Rogue River State Park. It's a great place for a picnic lunch. IF you have more time than the 3-4 days, Crater Lake National Park is a great place to check out, as is Mt St Helens in WA and Mt Rainier National Park in WA.
Big question here: Do you have maps? You need a map. A paper map, not the kind you see on a 5” screen (GPS or your phone) or a 15” screen (your computer). Since you are planning a multi-state trip, a USA map, regional map, or a road atlas of the US will do for starters. Take a pencil, some sticky notes, or other way to mark up the map: what do you want to see? What looks interesting? This is the most essential part of trip-planning, but unfortunately, too many people try to plan a trip without a paper map.
Donna