For teething you could try one of the white cloth napkins that she likes dip in water and wring out then freeze (in a food bag for cleanliness). It will be semi felixible and fabric like as it thaws and she chews on it (I'm pretty sure this is one of Tracy's BW suggestions). My DS liked that a couple of times but mostly he just used a plastic letter from his toy box (also never liked any teethers I bought for him).
My mum also thinks giving raw carrot a good idea but I wouldn't have done that at 6 months tbh. DS is now 17 months and can handle chunks of raw carrot coming off in his mouth but even though I did BLW, no puree at all, I just wouldn't have offered raw carrot.
Something that is very good if your LO will take it is raw celery though. it is less likely to bite off in chunks because of the long strands, if LO does bite then there are likely to be strands still connecting it to the long piece iyswim. In addition it is a natural anaesthetic so she will get pain relief from the numbness it offers as well as from biting down on it.
Teething aside. Staring fingers food at 6 months is a great idea even if you want to continue with purees alongside. Keep them in big finger sized pieces or wedges so that LO can grasp in a fist and eat the bit poking out the top. Avoid small pieces of food as these are far more likely to be a choke hazard (also in the early days avoid whole buts and small round fruits such as grapes and cherry toms as these are just the right size for choking). Offering exactly what you are eating is a good idea as it gets her used to the flavours that are family favourites and reduces fussiness, but it does involve adapting the way you cook, no salt (this is pretty important), no sugar, no honey.
Try any veg steamed or roasted, long pieces of meat or fish (must check for bones), fingers of cheese (or grated), fingers of toast.
Ensure that LO is sitting upright, no recline at all, for finger foods to avoid choking risk.
There's stacks of idea for finger foods on the recipe threads:
http://babywhispererforums.com/index.php?board=10.0You don't have to restrict to the 6 month suggestions, those who do BLW don't follow ages so 9 month + finger foods are also fine and there is a BLW thread of ideas too. Plenty of ideas to get you started.
Enjoy it, I have SO loved watching my DS learn to feed himself. Every meal I can't take my eyes off him because I just love watching him tackle his food with such enthusiasm.