You have certainly chosen a scene fraught with dramatic irony! Of course, before we begin exploring why this is so, it's always good to review the definition. Dramatic irony generally occurs when a character thinks one thing, while the reader/audience knows the reality of the situation. The dramatic irony of this particular scene revolves around Romeo/Juliet and the Lady/Lord Capulet. When Romeo and Juliet bid each other adieu in this scene they say the following:
Juliet: O, thinkst thou we shall ever meet again?
Romeo: I doubt it not; and all these woes shall serve / For sweet discourses in our time to come.
Juliet: O God! I have an ill-divining soul/Methinks I see thee, now thou art below/As one dead in the bottom of a tomb.
Even if it is an audience member's very first time watching (or reading) Romeo and Juliet, because this is, in fact, a tragedy and because of the indicators given by the chorus, we know that Juliet is right, they will meet again; however, it cannot be amid "sweet discourses" as the two surmise here, but amid despair and sadness. Further, even upon first reading and perhaps not knowing that Romeo will next be seen by Juliet directly in a tomb, this still can be seen as incredible foreshadowing.
Ironically, much of the dramatic irony in this scene has more to do with Juliet's parents than with Juliet herself. First, Lady Capulet misreads Juliet's tears:
Evermore weeping for your cousin's death? / What, wilt thou wash him from his grave with tears?
Even though the truth comes out a bit later in the scene, here it is clear to the audience that Juliet is pining for Romeo, not Tybalt.
Further, Lord and Lady Capulet are absolutely thrilled with the match of Paris and Juliet. Juliet's parents plan for her to wed Paris on Thursday! What we know: Juliet is already married to Romeo (and she wants a husband named Paris like a hole in her head, pun intended).