Maids are easily available in Brunei. All hours and wages are negotiable. Wages vary hugely, but expats tend to pay at the top end, typically B$300-B$600 per month for a full-time maid, B$100-B$200 per month for a part-time maid. Note that locals pay their maids considerably less than this.
Many houses come with maid quarters adjacent to the main house, and most people who choose to employ a full-time maid prefer to have her (and her family) live in. A live-in maid provides extra security, as she can look after the house while you are away, and it is easier for her to baby-sit or help out at odd hours, if required.
If your maid is a Brunei resident (red card holder), there should be no problem with work permits. Muslim maids usually will not work around dogs, and should not be asked to deal with non-halal foodstuffs, whether during food preparation or cleaning.
Many foreign maids are available. They tend to be green card holders and require someone to sponsor their “quota”, i.e. to pay for their work permit. Additionally, it is usual for an employer to pay return airfare to their home country once a year and allow sufficient time off for the maid’s annual leave. Arranging a quota can involve a large amount of paperwork, and it may be advantageous to employ a local firm to deal with this, especially if you are not fluent in Malay.