Oh she is lovely. Gave me a little tear, her face is quite a bit like my last girl's.
OK now. Chewing sticks is fine. Swallowing is not. You might have gotten off easy so far but sticks can be sharp and cause a perforation. Clumps of bits of chewed up stick might cause a blockage. My Jet, who your girl resembles, chewed but did not swallow. There was always a little pile by her stick, just like the piles under the woodpecker tree.
Our current Lab swallows so I have to remove sticks.
Because Jet loved sticks so much I actually gave her one. Remember, she is the one who did not swallow anyway. But I gave her a hunk of hard cherry from a tree we had to take down. Hard cherry is very hard and I wonder if a stick that hard might work for your girl. It would be more like a bone. She could still work at it but wouldn't be able to get as much wood off it at one time, therefore less to swallow, therefore less potential for trouble in the tum, tum tummy. The piece I gave her was quite large too.
My current boy is not much of a chewer but if he gets bored while I'm working in the yard he'll eat sticks. Not so much now that he is five. At your girl's age he was bored easily. So she might grow out of this a bit but I, personally, would not want to count on that. I'd be removing those sticks.
More pictures please.
Our Jet was pre digital camera. I don't have nearly enough pics of her. More of your girl please.