I think puppies AND DOGS should be allowed to walk without ALWAYS being made to heel. Knowing HOW to heel and what the command is will definitely be something you want to teach your pup, but in answer to your question, yes, she can have fun at this age and any other age. You might even want to start with the word "easy" if she is forging ahead or pulling on her leash, just to help her slow down and stop pulling when you communicate with that word. It might be helpful in teaching this word to use a little longer leash, maybe around 10', but not the retractable kind. This would give her some room to get ahead of you and then if she starts pulling you can give her a slight tug using the word "easy". Unless she is one of the more willful dogs, you should be able to communicate what you want in this way. As for when to start the actual "heel" training, I'll let someone else answer that.