Certainly, the concern that Romeo expresses at the end of Act 1, scene 4, before he and his friends go to the big party at Lord Capulet's house foreshadows later tragedy in the play. He says that his
Some consequence yet hanging in the stars [that]
Shall bitterly begin his fearful date
With this night's revels, and expire the term
Of a despised life closed in [his] breast
By some vile forfeit of untimely death. (1.4.113-118)
In other words, Romeo has a sort of premonition that the party tonight will initiate some series of fated events in his life that will culminate in his death as a young man. He, of course, is right. Tonight, he will meet Juliet and begin the relationship that will eventually lead to his suicide in her family's vault.
When Romeo and Juliet first meet and kiss, the audience knows that they are sworn enemies, although they do not know one another's identity yet. Juliet calls him "Good pilgrim," in part, because she does not know his name, and Romeo calls her "dear saint" (1.5.108, 1.5.114). It is only after this first encounter, where they fall in love at first sight, that each learns the other's identity. Their initial meeting when they do not know the other's identity constitutes dramatic irony because we know that they are sworn enemies before they realize it.
Later, in Act 2, scene 2, when Juliet believes that she is alone and speaking only to herself on her balcony, we know that Romeo is there, hidden by the darkness, and that he can hear everything she says. Because we know more than she, this is another example of dramatic irony.