Designing RESTful shopping cart

I am building a single page application for booking hotel conference rooms and am not sure how to set it up, or even if RESTful is the proper approach. There will be four steps to this SPA:

1. The user chooses a date (available dates come from server - some days could be fully booked).
2. The user chooses a conference room (conference rooms available at this hotel on the date chosen in step 1 are retrieved from the server).
3. The user enters their name, address, billing info.
4. User sees confirmation page.

This same SPA will be used by multiple hotels with the same database back-end, and for the front-end I was thinking Ember.

Is RESTful the right approach for this application?

I was thinking:

GET /dates?hotel_id=xxx (should I pass the hotel ID in the URL vs. in headers vs. in the body?)

GET /rooms?hotel_id=xxx&date=yyy (should I be passing the date and hotel_id in, or somehow remember it on the server?)

POST /order with body: {date, conference_room_id, name/address/billing info}, returns { confirmation_id }

Should the name/address/billing info be put into a separate POST?

Thank you for your advice.