Julie and Michael appear to hit it off, but when Michael realizes that Pam set them up on a date, he turns into his date character, "Date Mike," and things turn for the worse. She leaves after he talks to another woman, Donna.
Julie did not attend Jim and Pam's wedding, which suggests that they are not that close. It's possible that she was unable to attend the wedding, or that she became a friend after the wedding. The latter theory also explains why Pam hadn't set her up with Michael earlier.