A calm dog is a good dog. Unfortunately, not very many dogs are born calm. We have to teach it to them.

Your first line of attack is to teach her that the leash means "Be calm", not "OMG! We're going for a walk! I'm so excited! I have to pee!". Does your pup like human touch and massage? If so, just sit on the floor and start petting her in long, gentle strokes. As she relaxes, continue your massage to touch her paws, her head, her ears, her tail, etc. This way, she learns to tolerate handling and she will associate your touch with calmness. When she is sufficiently calm, keep one hand massaging her and use the other to clip the lead on her. Be nonchalant and calm yourself. Pretend it's no big deal. Unclip the lead and stop massaging. Repeat repeat repeat. Over time, your dog should relax more quickly. In the end, you should be able to touch her, clip her lead, and she'll associate those cues with being calm.

Once you are able to get her to be calm while putting the lead on, I have a feeling that actually taking her out will become much easier and less exciting, and she'll be less prone to peeing before you exit the door. If she doesn't generalize the behavior, however, I would suggest using puppy pee pads as a temporary training aid. Teach her to pee on the pads in the kitchen. Then, move the pads to the door. Then, move it outside. This way, your dog knows exactly where she needs to pee - on the pad.