I think you pretty much summed up what I was going to say. The "Leave it" command has to be one of favorite commands as it can be used for so many different things. keeping her on the leash also gives you the ability to take what ever it is away from her. I would use a 25ft long line to allow her to still wander but gives you control if she picks something up.Trading for a treat is a great idea.
Also, while she's still a pup, you could keep her on a leash in the yard and work on the command "leave it."
You CAN sort of do nothing, too. Instead of walking towards her, turn and walk back into the house. I can almost guarantee that, as soon as you're out of sight, you'll become much more interesting than whatever she has in her mouth.
hope this helps!