I always credit cycling with being a huge component in losing weight.
I started in January of this year, added a stationary bike into my routine in February and as soon as there wasn't a risk of frostbite started using a real bike. Cycling has been my primary form of cardio, although for other less intense exercise I also walk/jog the dog and started weight lifting in May.
An invaluable tool in addition to the actual bike was a heart rate monitor. While mine is a fancy GPS one to track things like speed, distance, elevation, cadence and heart rate there are inexpensive ones available. I started with a basic one and it truly helped. This helped me to make sure I was giving my best. Cycling can be a crazy intense calorie burner or a coasting delight. I've always opted for intense when exercising and wanted a way to track my progress.
I have taken my Jack Russell with me on the bike. It wasn't a great idea. He hurt his foot. If you really want to do it there are attachments
sold to do this. I personally think it can be too hard on both the dog and the rider. In addition, you will need to go somewhat slowly for your pup, but the dog will still get worn out rather quickly. I don't think it replaces quality time like a walk.
You'll be surprised how quickly your body changes once you start exercising, it probably won't be long until you're able to walk the dog without any major discomfort.
I walk my Jack Russell, the hyper dude, and it was never pleasant until I bought an anti-pull harness, now it's a walk in the park
I never had a trainer for my bike, like I said just used the stationary bike in the colder months. I bought it used for a good price and it was invaluable to me. It got me losing and moving!