I agree-- I don't think five minutes on the lawn is any more dangerous to a puppy without shots than to a puppy with. You just have to be careful and watch.
And when she's inside, I would definitely have her in the crate all the time, especially when she's just starting out on house training. So many people think that confining a dog to their crate will make the dog hate their crate forever, when it's really just the opposite. By keeping your puppy in her crate, you're likening the crate to her den and she will equate it with peace, shelter, and solitude forever. (Just make sure to make her time in the crate somewhat enjoyable-- a kong or some other toy will do the trick). By giving her full reign when she hasn't shown you that she can handle it, you're only inconveniencing yourself.