I assume you are trying to book this from home rarther than being in Malang now? I'd just tell them that you will show your passport when you arrive. I know it's common for accom places in Vietnam to hold your passport overnight, and some places in the other countries will ask to see it or at least want the number, but this is usually when you check in.
I always keep a laminated photocopy of my passport for this purpose and hand that over when I have to. The less time my real passport goes in and out of my pack, the less chance I have of losing it.
Also - I always avoid paying up front where possible. This way, if the place is a fleapit, is otherwise unsuitable or there is a screwup with your booking, you've still got your money in pocket.
I have been asked to provide a copy of my passport in advance in the past at more expensive hotels. I think it's normal, but I also feel uncomfortable doing it. Just tell them that you will do it later.
Thanks for your replies. I took the board's advice and told the guest house I was uncomfortable sending my passport information over the internet. To my surprise, they said no problem, and that they had already booked the room in my name.