Iwouldgoouttonight whether you will also get a 12wk scan will depend on how things work in your health authority.
In mine you get:
one dating scan (12wks)
one anomaly scan (20wks)
In some areas the dating scan is a nuchal scan instead, but they still date the pregnancy.
So if you are having a dating scan at 8 weeks in my area you wouldn't also get one at 12 weeks. If you need earlier scans here because of bleeding they are called viability scans and if the pregnancy is dated at one of those scans then you wouldn't be offered a dating scan at 12wks unless you had already got it booked, in which case they don't usually take it off you. As I say though, this is all just what happens here - different areas are different.
As for booking scans, in my area the midwife calls ultrasound and books them for you, or in rare circumstances will ask you to ring and book them yourself, but only if the midwife can't get one booked because you work awkward hours or are going away or something. In other areas you get a referral when you book in and will get an appointment letter through the post.
I'm not sure whether you will get another one at 12wks or not - it will depend on whether you get nuchal scans or not I think. But your midwife will be able to tell you for sure. Am also impressed that your doctor's surgery can do dating scans - very advanced!