In Act 1, Romeo is lonely and depressed. He is deeply infatuated with a girl who essentially shuts him down. However hopeless it seems, though, he swears he will never love another.
The rest of the play is all about his love for the other, new girl, Juliet, whose prime difference from the fair Rosalind is that she returns his affection and his advances.
While some might suggest that Romeo matures with his love of Juliet, I think his character does not change. The circumstances do, but he remains as intense and impulsive as he was at the beginning of the play.
Romeo is immature in his lovestruck adolescence. He thinks he loves Rosaline, and her refusal to accept has him hiding away from people, and spending all his time alone.
He very quickly switches his affections to Juliet, but does seem to mature a bit as the play continues. He is more serious than the other young men, and does appear to think things through.
At the news of Juliet's death, he takes the time to think of how to die with her, and puts it into action. If he continued on the course he started, he would have forgotten Juliet and fell in love with someone else.
In Act I, Romeo is depressed because Rosaline does not respond to his love. But we later realize that the 'love' he feels for Rosaline is nothing more than lust because it suddenly disappears when he sees Juliet. But what he feels for Juliet is real love. Actually, throughout the play we see the switched roles of Romeo and Juliet. Juliet is always rational but Romeo is childlike. I think Romeo behaves maturely just when he arranges the ladder to Juliet's room because if they do not become husband and wife, the promises they give to each other would mean nothing to Juliet's parents. But if she loses her virginity, it would be harder for the parents to seperate them.