Teddy (the dog) was a rescue, he was about 6 months old when we got him - so he was just the cost of the rescue. He is a very nice, very tolerant dog, great with the kids. But he is as dumb as a bag of rocks. I thought that a golden doodle would be smart - poodles are smart, goldens are easy to train. Not our dog though. He will sit, and sometimes comes when called. Thats it. I had border collies and siberian huskies growing up. I had a cat trained on voice commands. I had a mutt that knew over 30 individual commands. Teddy only sits. He won't even fetch. If you throw a ball he looks at you like you are insane for throwing his things. I've heard from several folks that their 'doodles' were not intelligent dogs.
Golden Doodles do shed, almost as much as a golden retriever - it just depends on what 'blend' you end up with.
I've never had a Rottweiler. I think I'd like a German Shepard next, something really smart and easy to train. Or maybe a Great Pyrenees. Or an Old English Sheepdog....