SJ- my wife was 37 and 41 with ours (both through IUI).
I'd say to relax about this if at all possible. Can't hurt to find a doc now, if just to find somebody you like for 6 mo from now. Our doc in NYC was super busy, but readily available if that makes sense; wife could mak an apt close to the day, but usually had to wait in the doc office for a while.
SJ-My wife was like yours, nervous and impatient from the get-go. She had reason to be; she was an only child and had some concerns about whether she'd be able to have a baby after 35 or so because of her mom. We got married just before her 30th birthday (I was 36) but she still pushed to crank up the process quickly. So she started looking to see a doctor almost immediately. I'm glad she did, because it ended up taking us 2.5 years to get a bun in the oven.
The one year thing is probably tied to insurance coverage. We met with a fertility expert after about six months. My wife explained her concerns and also that we didn't want to pay for anything drastic/expensive yet. He ran some tests on both of us (side note- least enjoyable solo session EVER) and started her on some relatively inexpensive fertility meds. That way when we got to a year, we'd already exhausted those less "extreme" options and were ready to move to some of the more drastic/expensive stuff like IVF. Still took us another 18 months and my wife resigning herself to an egg donor to get it done, so I'm really happy she started it up so quickly, even though at the time I was hesitant.