I would definitely have her assessed - even if she doesn't test as gifted you'll learn about how she learns, and that's worth testing if you are able to afford it.
Re gifted and recognizing it - gifted can look so different in different children, as others have pointed out above. In my own kids, my EG kiddo was so obviously highly intelligent - to anyone he would actually have a conversation with - but he was extremely quiet at school and with adults when he was younger, and he also is 2e with written expression challenges, so he actually had a teacher in 2nd grade who thought he was on the low end of the IQ spectrum. Our youngest dd is HG+, and she struggled to learn to read. Our middle dd is on the very low end of gifted if that (she's had uneven IQ tests), yet she is an avid reader. There's simply no way to describe all gifted kids in one bundle - they are all individuals.
The one thing that happened with testing for us though that was really helpful - we had never thought of our middle dd as gifted (and still have questions about it). She had an IQ test as part of an evaluation for anxiety when she was young - at the time we honestly thought she was perhaps challenged intellectually in some way due to some of her behaviors at home, and she always had her older brother and younger sister stepping in and answering questions for her so we thought she was stumbling and/or slow or not able to answer the questions. She tested MG at that time and no one was more surprised than her parents lol! But we noticed something happened after we had the test - we began to treat her as though she was gifted and she responded in a big way, so for that, whether or not she really is gifted or not, I am very thankful that we had the test. Her scores since then haven't been high enough to qualify for gifted programming at school, and she sometimes asks why her brother has had opportunities through school that she hasn't, but overall, it's been good (I think) for us to think of her as gifted. The psych who tested her also pointed out that we (at the time) might have thought she wasn't gifted simply because the two kids who were answering all her questions for her were HG/EG whereas dd was MG.
Best wishes,
polarbear
