Since the poem is called "Upon Julia's Clothes," we should expect to meet Julia. And she's quite the lady, or at least her clothes would suggest as much. In fact, we may meet Julia, but it's her outfit that leaves the lasting impression. The woman herself is just about synonymous with her clothes, which are described as flowing, glittering, even vibrating.
We're guessing Julia's personality may be in some ways like the descriptions of the clothes (in the speaker's mind at least). Maybe, Julia is a bright, graceful, and charming person. Of course, the speaker doesn't give us a whole lot to go on, so we'll have to rely on our imaginations.
Line 1: The speaker prepares to describe his experience of watching Julia walk by, dressed to the nines. "Goes" seems to be doing double duty here. It describes both Julia's actual, physical motion, but it is also a metaphor for wearing clothes. It's kind of like when we say "I'm going to go with the blue pants tonight" to mean "I'm going to wear the blue pants."
Line 3: The speaker refers to Julia indirectly by mentioning her clothes. He's watching Julia walk by, but it's her clothes that are doing the moving.
Line 5: The speaker again seems to refer to Julia indirectly by mentioning the "brave vibration" of her clothes. That brave vibration is a metaphor for the movement of Julia's silks.