Are you interested in a modern wooden concert flute, a baroque flute, or a flute from a different culture? They are totally different beasts from each other.
The Modern Concert Flute:
It was in the early 20th century that metal flutes became the standard instead of wood due to the superior projection and tone colour offered by metal flutes compared to wooden flutes. In recent times though, advancements in instrumental technology have led to the development of modern wooden flutes that combine many of the finest qualities of metal flutes with qualities that can only be found in wooden instruments, and a small percentage of professional orchestral players choose wooden instruments now. The percentage is higher on the continent than in the UK, but at present metal is definitely the norm.
I think Daniel Pailthorpe from the BBCSO is the highest profile UK player who plays a modern wooden flute. Here him here in this performance of the Poulenc Sextet:
It is my feeling that wooden instruments have very clear advantages over metal especially for orchestral playing. The top register in particular has a more mellow quality but still with projection, that seems to make the flute a more natural member of the woodwind family. The effortless way the flute sits on top of the other instruments in this video shows that very well - it is exceptionally tough to achieve this to the same degree on a metal instrument, it takes a great deal of persuasion from the player!
I don't know what model Daniel plays but can only assume it would cost many, many thousands.
Here are two of the biggest names on the continent who play modern flutes:
Sebastian Jacot is the most famous student of Jacques Zoon. I believe Jacques Zoon made his own flute, or at the very least was very involved in its production, and Sebastian plays a copy of it. As such their instruments are pretty unique.
I must say I LOVE the sounds of these instruments, and sometimes feel tempted by a wooden flute, but it is an indulgence I cannot really think about right now. I have tried out one or two in flute shops, standard models like Powell, so less special than the likes of the instruments above, but even these were at least £6K. I remember appreciating the qualities I described above in terms of an instrument that would work well in an orchestral setting, but the trade off at least on the ones I tried was a slightly reduced projection in the low register.
I have a suspicion that we are going to see them gradually become more commonplace in professional orchestras over the next decade or so.
In relation to your other questions on them, I think in terms of keywork the feel is pretty much the same as a standard metal flute so small hands should not be a problem. In terms of care, I play a wooden piccolo, which needs to be oiled occasionally, and extreme cold conditions can be hazardous. It is best to keep wooden instruments played regularly - they take a bit of playing in again if neglected for too long! So I would imagine a wooden flute is similar - it needs to be treated with a bit more care but not a major issue.
I have posted this info not just for the OP but for the general interest of anyone reading. If I speak really bluntly, I would suggest that at least for most grade 6 standard players, purchasing a modern wooden concert flute would be a very indulgent purchase. Obviously it is a major investment, and in my opinion such investments are best made when you have enough experience in pushing the boundaries of the instrument you already have to really know what you are looking for, which will likely change as you develop.
I have actually never played a baroque flute but in short, the period instrument revival has meant that there are now far more baroque flutes (copies of the instruments that were played at the time) than ever before, popular with professionals and amateurs alike. Although I haven't played one, I know they are very different to play. Crucially they don't have the modern keywork system, but a more simple system of holes for the fingers like a recorder. More complex fingerings therefore have to be employed so there are many new things to learn about playing one. Some notes in particular take more persuasion to play in tune. Many baroque flutes are tuned to a lower pitch so if playing with other instruments, you can only play with instruments tuned to that pitch. Some baroque flutes at modern pitch do exist though.
I don't know the costs, but I am pretty sure there is a wide range of prices out there, and it needn't cost the earth. For players with a particular interest in baroque repertoire, a baroque flute can be a worthwhile purchase. It certainly sounds very different to the modern concert flute arguably closer to the sound of the recorder - listen to recordings to decide if you like the difference (here is an example: https://www.youtube....h?v=2gSb7s75tbE).You just have to choose with care whether to go for one at A=415 (lower pitch) or A=440 (modern pitch) depending on what instruments you might get to play with the most. And you have to be ready to take time learning the new fingerings and getting used to the different style of playing and sound. At least a couple of lessons with an experienced baroque flute player would go a long way.
I'm afraid I don't know if a baroque flute would be problematic for small hands. Perhaps somebody else will have the experience for that question.
Many other cultures have wooden flutes, such as Irish flutes, Chinese flutes etc. A friend of mine has probably over 100 wooden flutes that she plays a lot in shows, so I can only assume they don't each cost a fortune! So as a different experience with novelty factor, that is another thing to consider.