I have had good luck.
Our dog has flown a couple of times from the Lower 48 to Alaska without incident.
Each time it seems like the dog gets better treatment than us pax! I've watched the dog be carried on a cart by itself, given water, etc.
Alaska also has a program where each time your animal is put on each individual flight, they bring you a tag for your particular flight. It sure sets the mind at easy knowing your animal is on board.
Realize that if it's around the holidays (November/December) that Horizon will not transport your dog at all, period, end of discussion. So watch your SFO-PDX flight if it's operated by Horizon (I think all currently are) and happens to be around the holidays.
And they have too-warm cutoff temperatures as well in the summer where they'll refuse animals, for good reason.
I know there are horror stories out there about flying with pets, but I've had good luck.