We have a 10 month old Australian Shepherd/Border Collie mix. VERY smart dog. She chews everything you can imagine and knows it is wrong. I can not leave her alone for 1 minute. (literally) We have to crate her during the day (work) and again at night (sleep). I walk her (leash train) every day for approx. 1/2 mile walk and practice sit/stay and down/stay for 10 to 15 minutes every day. Everyone says exercise is the answer. So about a month ago we added to her regimen a 1 to 1½ mile run 5 or 6 times a week. Did not faze her. She is getting plenty of exercise but she still chews everything in or out of the house if she thinks she is not being watched. I took my eyes off of her for 1 (only 1) minute the other day and she chewed up the corner of a rug. If she is outside, I (or someone) have to be outside and watch her. If she is inside, I (or someone) have to be inside and watch her. I set her up to catch her chewing so I can correct it. I do the alarm/no/command and she stops until she thinks no one is looking. Then she will go right back at it. When something catches her eye, she will actually look for me to see if I am watching her and if she does not see me, she goes for it as fast as she can. I am getting really frustrated. Not to mention, I am exhausted.
I understand your frustration. You can not watch her all the time and yet you can not keep her in her crate all the time...
I agree with the idea that she needs exercise but it does not only mean physical exercise but also mental exercise. I think your puppy is under challenged, especially because of her breed. Both Aussies and Border Collies are known to be very smart and they are working dogs!!
There are 2 things I would like to suggest:
1) Get a dry bone and put some wet treat in the hollow. Or you can use a Kong. Every time you find your dog about to chew something, call her and give her the bone or Kong. In other words, teach her what is OK to chew and what is not.
2) Your dog can learn a lot more than sit and stay. How about fetch, or some tricks/games. Here is what I do with Holly and Noah, my border collie mixes.
The game I do with Holly and Noah inside the house is quite a fun for both me and the doggies: I have my dogs wait in the living room. I have a bunch of stuffed toys and I take a basket full of toys to another room and scatter them all over. I come back to the doggies and say "Go get your toys". They bring a toy back to me one after another and I give them a treat each time. We repeat this until all the toys are back in the basket. Dogs get some exercise by going back and forth the two rooms (and I usually put a big box in the hallway so that they have to jump it over each way) and they are happy and eager to play this game because I give them a tiny bit of treat every time they bring a toy to me.
I like reward based training because it is fun and motivating. It will take a little time for your dog to learn this game but "practice makes perfect". Work on it a little by little. Because a simple game like this consists of quite a few behaviors: First, Wait - then Go Look for a toy Jump the obstacle - Pick it up in her mouth - Come back to me with the toy - Jump the box again - Hand me the toy or Put it in a basket. They need to learn the sequence of those actions. They learned it for fun and a bit of treat!!
Start with "pick up the toy" with your dog. Have her sit in front of you, lay a toy in front of her. Say "Leave it". Give her a treat if she leaves it. Then tell her to "Pick up" (or OK) and give her a treat if she picks it up. You can also practice "Take it" and "Drop it" alternately.
By doing the 2 practices mentioned above, I hope your dog will stop chewing things that don't belong to her. It might take time but please be patient.
