I am also pregnant and have only been in the country for just 4 weeks. I have already gone to the Al-Ahli hospital for my first appointment and things went nicely. I will be giving birth there as planned. They also have a pediatrics clinic there as well so everything can be taken care of onsite. I have taken my 18 month old to the clinic and things went very nicely and the doctor was nice as well.
When are you due? If you have any questions about pregnancy in general let me know. I'm no expert but have given birth and do know what to expect.