Camping while pregnant

Okay I know this might sound crazy, but we are trying to do some sort of vacation that isn't expensive. We live in California and wanted to drive down to New Mexico for the caves and sights etc. I'm currently 23 weeks, and in order to save money we would stay at camp sites instead of hotels. Does it sound reasonable? If not do you guys have any other "fun and cheap" vacation ideas. We like in LA. 

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