1) How long would it take to get married at the embassy in Qatar
a. It depends on your embassy some embassies defined couple of days in the week for the marriage and for divorce as well.
could that be achieved in a weekend (shot-gun wedding or what!)
b. yes it can be done in one day and pick the marriage certificate after max 3 working days.
1) If we get married then will my GF (or should that be wife!?) be able to transfer her contract to married status without issue?
a. Yes, but the status change has nothing to do with being bregnant or not, it is matter of getting better contract if her employer has this class in HR system
2) If the contract can't be changed then will that present issues at the time of birth
a. No
- i.e. she would have to show marriage certificate to authorities  yes she has to show it up
. Work could terminate her because she's on single status contract etc.
3) If the contract can be altered then could she sponsor me as her husband so I can move there for work.
a. Yes she can
4) If the contract can be altered how long will it take.
a. It depends on her employer
5) If the contract can be altered can we apply for a family visa so I can
a. Yes you can