Hi Bea,
CONGRATULATIONS!!
Yeap, it's a good place to start, see your GP. You will need to be taking folic acid if you're not already. Your GP can prescribe it or you can buy it from the pharmacy (although it's cheaper on prescription).
Your GP will probably have pamphlets for MWs in your area. You will probably get a blood test done and maybe another urine pregnancy test.
I *think* an OB is more important in riskier pregnancies? Most people just use a MW as if there are any problems they can put you under the care of appropriate people.
I'm not sure if you will have to pay for medical care, it's free for nz citizens, don't know about visitors sorry.
Best of luck for a happy and healthy pregnancy