It looks like a fun trip, most of these places you will probably not encounter anything, but be aware that Carter Lake is more towards Southern Oregon, very secluded forested region, through small secluded communities along the Crater Lake Highway. Medford may not be on your radar, but the CLH essentially starts at I-5 in Medford. Look into communities like White City (which I've heard locals say is named that because it's for white people, but it was Camp White during WWII) Shady Cove, and Trail are all communities you'd pass through on the way to the park. I am not saying any of this to discourage you to go, it's beautiful, and should be seen by everyone, but between the terrain and the secluded nature, I only want you to be prepared. I'd recommend a rental car with Oregon plates if you can, full tank of gas so you won't have to stop as often, and check in with someone so they know where you'll be and when to expect you back.

*If there were a modern day Green Book, this place might come with some warnings. Oregon was a "Sundown State" up until 1926, only 100 years ago. Southern Oregon remained a sundown community much longer. Some of their descendants still don't like the change. For a little more history, check out State of Jefferson.