I went to the doc for the first time around 9 weeks, but my first ultrasound appt was at 12 weeks, so I think every doc chooses to do things differently.
My ob does 2 u/s: one at 7 weeks to confirm pregnancy is in utero and one around 10 weeks to check development. I also did a screening for Downs at around 12 weeks and then the big u/s came at 18 weeks. I know that in many cases insurance only covers one u/s around 16-18 weeks. Did they check for heartbeat at your last check up? if the h/b was normal then everything is OK.
Good luck!