We're about to take our youngest (10 weeks) away for his first camp and decided on one of these from eBay. It's basically a really small dome tent and packs down to about the size of a sleeping bag.
You can get a sunshade for it too, so you can "pitch" it outside or on the beach during the day. Fingers crossed all will be fine.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.