First doctors visit. PLEASE ANSWER

Kristi • Proud new mommy to a gorgeous baby boy born May 6, 2015.
I'm 6 weeks along and just found out I'm pregnant less than a week ago. I just called the low-risk prenatal care clinic and they aren't getting me in until October 3. Is it normal to wait that long for a doctor visit? I'm just worried as this is my first baby and I want to be extra cautious.