The only form of ID which is accepted for security purposes by ALL airlines is either a passport or a National Identity card. (UK National ID cards are currently only available, under a pilot scheme, to residents and workers in the northwest of England).
If, for example, your sister wished to fly with Ryanair she would have to obtain a passport (or, if her home address is in the northwest of England, a National ID card). However the Birmingham to Inverness route is operated solely by FlyBe. Acceptable forms of ID for FlyBe's domestic services are listed here:
http://www.flybe.com/...o/id_requirements.htm
You'll see that a Citizen Card is an acceptable form of ID with FlyBe. That's probably what you've been told about (since I've seen application forms in some Post Offices). It's primarily a 'proof of age' card but anyone can apply for one. (The cost is £15, or £30 for an urgent application). The FlyBe webpage includes a link and a phone number.
Chris