Natellie1970 - if you haven't already skulked off with your tail firmly between your legs I would like to draw your attention to the following thread:
www.mumsnet.com/Talk/gifted_and_talented/a1841855-Difference-betwey-aen-G-T-and-bright
This is where I have used this thread to illustrate an earlier post I made on the above thread - about the oft repeated views on the MN gifted thread regarding bright v gifted and how advanced reading is no indicator of giftedness.
Over and above reading 4 years above her chronological age (well done your dd) you mention her being both quick witted and a quick learner and reaching at least one milestone (her first word) early.
Seemingly only the profoundly gifted are considered gifted on this thread (many posts, although by no means all, attest to this). My view is that a child with an IQ of 120+ is gifted, with increments going through moderately, highly and profoundly gifted.
You can look here to get more of a sense of this yourself. It is not a definitive science and people may ague about the methods of determining giftedness.
Of one thing, however, I am clear, there is no jump straight from bright to genius level giftedness - there's a whole range of gifted in-between and my view (for what it's worth) is that your dd likely sits somewhere in this in-between range.
If she is doing well at school then you need to do little other than enjoy her and stimulate her by supporting her with her passions. If there is a disparity between her 'smarts' and her performance at school, well it's definitely worth exploring it with them.
All the best 