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I presume a 13 year old western girl can dress 'normally' in the compound and at school.
What about in between and in the shopping mall and arriving at Dammam airport?

northbadawi

In the compound - females can dress "normally", even bikini, at school kids usually have uniforms.
In tinted car in between - no problem.

In the streets, shopping malls, restaurants and all other public plases - abaya is a must, head cover - no.
At airport in between the arrival and taxi - not a big problem if dressed modestly.

dragonladyoz

I have known western 13 year olds that do not wear the abaya in public - and others that do. It pretty much comes down to will she attract male (or muttawa) attention if not dressed in the abaya? i.e. does she still 'look' like a child or is she well developed? as mentioned - head cover is not required.

scot47

No abaya needed but "modest dress" is advisable. Khobar is "liberal" and on the same wavelength as Jeddah. Certainly no need to cover when travelling from airport to compound.