Every one of mine started camping before they were walking. The first three in tents, the last one got the trailer. I like the San Diego County Parks and by far my favorite campground when the kids were little was Dos Picos in Ramona. But really that's when they were a bit older and could ride their bikes with training wheels and such. I guess it might depend on where you live in San Diego. Ramona is a bit in the mountains so it can get colder at night than somewhere like sweetwater Reserve. Burnt Rancheria up in the the Lagunas is nice, but probably closed this time of year. You could always go to Santee Lakes which is really popular although I've never been. Or Chula Vista Resorts which I think is a KOA. Personally if it's your first trip with a baby I would try to stay within 45 minutes to an hour from home.
Sitting here thinking about this reminds me of my first son's first camping trip. We were tenting in Burnt Rancheria and he was probably about five or six months old. At the time the entire campground was no facilities just pit toilets. Somewhere around 3 in the afternoon he had one of those explosive mushy diapers that ran all the way up his back and even got into his hair. Being in a tent with no facilities we just packed up and went home. Had we been closer I might have taken him home for a bath and fresh clothes and then back to camp.