D.T.
I don't understand why you don't think she can't have what you're eating. By age 1, kids are more than capable (and should be!) eating normal food so whatever you are ordering should be fine. They may not have the molars yet for chewing but they can gum anything... none of my kids had a single tooth until after their first birthday and they were eating normal food (ie, what the rest of the family was eating) by around 8-9 months.
Try to go early, like around 5 or 5:30 when there's no waiting. Or feed her at home before you go so she might be more intersted in playing with toys instead of eating. Or, just gracefully give up for awhile -- don't go out for a few months. Age 1 is tricky at a restaurant simply due to their development.... most 1 year olds simply can't control themselves. They want to move... 15 minutes of sitting at a table is pure torture for many. I know some can do it, but the majority of 1 year olds are simply not developmentally ready.
On the rare occassion we went out to eat with a 1 year old (like when travelling), we had to tag team it. We would sit down to order with toddler on one of our laps. Then my husband would take the child on a walk around the restaurant and to the lobby area until the food arrived. When food arrived, we'd plop the child in the highchair, give him/her some food from our plates and eat quickly. We would be done and ready to leave about 20-30 minutes after the food arrived. We found each child had different limits. Our son had a 45 minute limit in a restaurant... if we left before then, he was fine and it was a pleasant experience. If we took 55 minutes, he was in an all-out meltdown that made everyone miserable. Our 2nd child could make it an hour and our youngest is still pretty portable and doesn't care.
With each child, though, by the time they were 2.5 they were great in restaurants. We don't go out to eat often... maybe once every 2 months. Some people believe you must take the kids out often to teach them but you do not. We insist on table manners at home so when we go out to a restaurant, which is a rare treat, they know how to behave. We don't like going out to eat often because most restaurnt food is too expensive and even the 'healthy' choices on a menu are much more nutritious if made at home.