A 2 month old puppy really doesn't need any formal exercise and is too young and not fully protected by vaccinations to be out on the ground in public. What activities are you already doing with your pup and then we can make some suggestions
A puppy of 2 months doesn't need to be walked. She shouldn't be allowed on the ground away from home, even, because she won't be protected against very dangerous illnesses until she has finished all of her vaccinations. You are putting her at great risk by doing this. Instead, you should be playing and doing brain games with her. From simple training (leave it / sit / stay / recall etc) to hiding bits of her food around the house for her to find. Anything that exercises her brain will wear her out far more than walks ever will. Training sessions should be kept short - no more than a couple of minutes at a time, but several throughout the day. Here is some information on appropriate exercise for puppies: http://www.thelabradorsite.com/labrador-puppy-exercise-how-much-is-too-much/ and some ideas of what to train: http://www.thelabradorsite.com/ages-and-stages-in-labrador-puppy-training/
OK, off the top of my head, you can be teaching in very short sessions things like sit, come, down, stand. Practice handling the puppy all over - ears, teeth and mouth, eyes, paws, legs all over the body (your vet will love you for it ). Then you have things like sit and wait for release before going to food bowl. You can be teaching a settle on a mat. You can start on a sit to greet people instead of jumping up. You can play little tug games and retrieve games. I'mean sure others will be along with other suggestions. There is just so much you can do but it's for you to decide what is most important to you and your life/family.
I believe you can and should go for short walks at that age. (10 minutes at that age and slowly increase) These walks should be in rural areas away from places where other dogs go. Be quiet on the walk and let the dog follow you.... this will create a responsive attitude that will help in many other areas of life.
When Molly was very young she loved scrambling in and out of cardboard boxes -as well as chewing them up. Another activity was chasing around a plastic bottle, into which I'd put a few pieces of kibble -eventually they fall out to be eaten. I also tied an old sock to a length of rope and let her chase it as I dragged it around. Then when she caught it I let her have a brief chew before swapping it for a treat and then the game started again. We only have a smallish (60foot) garden but it's informal (good word for tatty!) and in those early weeks before she'd had all her vaccinations I spent a lot of time outside with her, which kept her amused with chewing things, carrying things around, digging etc.
This is what we did. I'm lucky to be in a rural area with a choice of places that other dogs didn't go to, or not much anyway. Partly because it was an unusually cold and snowy winter and I don't know what all those other dog owners do but they sure don't take their dogs out much in winter. WE were off leash till vaccinations were completed at 18 weeks and then went through our small village on leash. Mostly we played.
Hi Jeimer, you have had great advice above. One thing that DH and I did with Harley was to stand a few meters apart, each with some of her dry food in our hands and we would take turns calling her name and giving her a treat and lots of praise when she came to us. This a very hard work for a young pup so we kept it down to about 5 mins. We used the game to start teaching her to gently take a treat from our hands, and also to start with sit. But all very low key, it was more about her being an awesome pup that was so excited to come to us. Now that she is 5 months we still do this, only with much more distance. She still loves it.
My puppy is now 12 weeks and in the past month, we have done so much. The empty plastic bottle is a great one as she goes chasing, tossing it around and I put some kibble in. Cardboard tubes to rip up - messy but satisfying for her. Each day, I brush her teeth or more like she chews the toothpaste off the brush. I know she will lose these baby teeth but it gets her used to having her mouth touched. One of those cylinder kings with some kong paste in the grooves. Feeding ball that she has to push around to get her food out. Brushing her coat a couple of times a day and getting her used to being stroked, tickled, touched. Outside for running around and the beginnings of recall, going down, sitting etc. Inside for all these things plus settling on her bed. All activities for a short space of time separated by time resting in her crate and of course all the time taken up going outside to toilet and get praised.
