We’ve booked to go away camping for two days during the summer. Our puppy would be 12 weeks old and fully vaccinated. I was planning on bringing the play pen and crate with us which she’d spend most of her time in, in the day tent. At night I’d sleep next to her, with her in the crate. I’d of course make sure that she doesn’t get too warm (maybe with those electric fan things) and would limit exercise, giving her plenty of time to chill in playpen/crate so she doesn’t get too overwhelmed.
We did it with our 12 week old in caravan. All fine and we'd only had him 5 days. Only thing I would check is how long after vaccinations they become effective. Ours wasn't so he was still carried around in rucksack