Replaced 1 tire but should I do all 4

If it were me, and I had the money, I'd replace the rest of them now including the spare. If I was short of cash (and who isn't these days), I'd wait until next spring per your original plan and use the one you just bought as the spare. But I'd take a close look at all of the tires for any deformations, cracks, etc. every time I stopped. We've caught a few tires early before blowing out just by looking at them and running my hand along the tread. It was pretty obvious they were coming apart. My experience was once the first one came apart and blew at 4 years old, the others soon followed. It started to seem like every time we took the camper out, we had a tire go. Even the spare, which had less than 1000 miles on it even blew. We got lucky in that other than some black marks, only one blowout actually caused any damage when it ripped the plastic fender off the camper.