It sounds like it could be what is called "submissive urination". Here is a link to an article about it and you can google the term to read more articles and info. If it keeps up as the dog grows or begins to happen during other periods of excitement or anxiety, I would start to correct it early before the dog becomes habituated to doing it.
Most dogs won't urinate when seated or lying down so if you teach your little one to sit or lie down before you are going to do something potentially exciting or scary, it can help. It's not a cure all but it helps. Then, working to build up the dog's sense of worth and self-confidence with good behavior reshaping through positive reward obedience training can give your dog a good sense of achievement and confidence. But keep your training sessions upbeat/fun, short, repetitive and very rewarding for the dog - praising for doing it right and a little treat, big smile. I agree with the article that the
Nothing In Life Is Free programs you can find for free on the 'net also helps your dog not to fear but respect you as his leader and give him self-confidence as he learns to work and obey to commands and it helps to make a good team of the two of you.
Dog Submissive Urination