Is there a room downstairs that could be converted into her bedroom? Maybe it is not so much fear of burglars, but fear of being so "far away" from Mommy and Daddy? How is she during the day? Does she play alone in her room? Can she nap in her room?
My son used to refuse to sleep in the spare bedroom at my Aunts because it was in the front of the house and had two floor to ceiling windows. He used to say someone "might steal me". So she finally moved all of his things into the back bedroom - still had a window but it overlooked the fenced backyard - and he was fine.
When I bought my house I let him pick which of the two "childrens" room he wanted because both faced the street and I was really worried he would not sleep in either and I was going have to give up the master LOL. He picked the one with the big bush in front of the window so "people can't see me". He was 11 then. He still gets a little nervous whenever I have that bush trimmed in case it gets too low.
Maybe have a night time routine with your daughter that includes setting the alarm and checking the door locks and windows - I did that with my son for the first few months after we moved in....he now checks the door locks for me. :) Establishing a little "ritual" of night time lock up may held allay her fears. Also, have you ever set the alarm off so can hear what kind of noise it makes? If it makes sirens? Obviously you don't want to do this without notifying the alarm company so police and fire don't show up at your door.
And, most importantly, talk to her. Find out what exactly frightens her and then keep an open dialogue. You could also explain that you and your hubby need adult time and that no-one is getting enough sleep. She is old enough now that you can begin working through this fear with her.