I think it's fine to bring them because as elegant as it might be, you're still at WDW where kids are widely accepted. They will definitely have high chairs for you, bcause even if they do not have them right there, the GF has other restaurants that have highchairs so I'm sure they would borrow one for you. Also, you could also put her in a regular chair if you really had to and I'm sure she'd be entertained with eating and you being right there. Now, if you were planning to let her run around wildly without supervision, that would be a different story, but since I doubt you are planning to do that I would bring her.
We went to the California Grill on NYE and considering the extremely high prices, service, and food selection, you wouldn't expect to see kids there. There were many little kids, however, ranging in age from 15 mos-9 years, and then many preteens and teens too. Though it was a very elegantly done celebration there were lots of kids and I did not feel they took away from my enjoyment of the evening at all. And most of these little kids were left to play by themselves all night, at times taking over the dance floor and joining in with the hired entertainment, but I didn't see that as annoying at all. It was actually really cute to see them dance around with each other. They also served peanut butter and mini-marshmallow sandwiches cut into triangles for the kids and set those out right in between the 'adult' foods, like sushi, cavier, and filet mignon. If they didn't want kids to be invited, they would have specified that, so I wouldn't worry about it.
So I wouldn't hesitate to bring her along, she'll have a great time and you'll get some supercute pictures of her enjoying her tea!