1 bedroom places aren't that common and tend to be expensive for what you get compared to a house outside of town.
A friend of mine who works as an agent says they know of a few in the Dahra part of town for between 800-1200LYD/month, but that for 800LYD you shouldn't expect much. Don't imagine this is going to be like a Western style studio apt.
A problem you may have is that most landlords want 12 mths rent up front. I'm just helping someone negotiate a 6 mth rental, but it's not been easy and many landlords won't consider it. It might be worth looking into a long term stay at a hotel for around 80-100LYD/day. That'll solve the issues you'll have around safety/rental/bills etc.