I'm probably 4 or 5 weeks pregnant

So I took a pregnancy test on my birthday which was on September 1st and it's positive! I'm so happy! My family wants me to wait until I'm 4 months along to go see a doctor but my boyfriend and his family want me to see a doctor by the end of the month. I did some reading on the internet and many women said they didn't go to the doctor until they were 10 weeks pregnant and they were just fine with healthy babies. I'm 33 and this is my first baby and I want to have a healthy baby. Is there anyone out there who waited a long time to see a doctor when pregnant?