You can, but it sometimes gets culturally awkward, so we recommend staying in accommodations if you have the budget. It benefits the local economy, and you can travel with a much lighter luggage. For each stage there is usually a wide choice of accommodation, ranging from simple home stays to more luxurious five-star hotels.
See Accommodation for more info.
Since camping is a relatively uncommon thing to do in Jordan, and it would be culturally completely unusually for a group of women to camp out all by themselves, we strongly advice female-only groups against camping! It would most likely attract the attention and curiosity of shepherds or other people passing by, and may lead to uncomfortable situations.