When did you have your first scan??

Last time I was pregnant I was young and was going for an abortion and had a scan at 7 weeks. I miscarried a week later. 
I just had my first doctors appointment 5w2d and she said since I'm keeping it this time I won't get a scan until the 13th week?? In New Zealand maternity care is paid for by the government so everything is free but she said if I want an earlier scan I have to pay hundreds of dollars. I'm so nervous having to wait so long until the first scan!! Would you recommend paying hundreds to see potentially not a lot??