Okay, since no-one else has answered, I'll give it a whirl. I'm at a similar stage to you as dd2 is 7 months, and was bfed exclusively till 6 months.
I don't think your idea of cooked carrot sticks is barmy, let us know how you get on. BUT the transition between bfeeding and 'real' food, whether purees or chunkier finger foods is not as obvious as it seems, since it requires completely different tongue action. dd2, bless her, spent the first week of weaning pushing everything straight back out, simply because she couldn't work out how to use her tongue to move it to the back of her mouth ready for swallowing.
With proper solid foods, like carrot sticks, you have additional problems inasmuch as they have to keep hold of it long enough to 'eat' it. I would have thought there is also a risk, if they are soft, that the baby will bite a chunk off with its gums and choke, which may freak you out and/or upset the baby.
Also, be warned, IME experience bfed babies show a strong preference for very sweet food, so carrot sticks may not cut it.
Since dd2 is my 3rd child I'm quite lazy about making stuff for her. Things I know she'll always eat are petit filou yoghurts and an instant rice porridge called Cerelac (made by Nestle, tragically -- how un-pc can you get?) Having said that, I've never found that the quantity of solids consumed at teatime had any direct link with sleep duration, so it probably doesn't matter from that point of view.
Ds was also quite conservative in his early tastes (banana, banana and banana), but on holiday aged 9 months discovered tapas in a big way. He snarfed chorizo, olives, squid, artichokes, at the age where most of my friends' babies were still eating glop from jars.
Summary of my ramblings -- go for it, but be prepared to change your plans as you go along. They'll wean themselves off bmilk sometime before starting school whatever you do.