There is definitely a sense that Romeo is immature and infatuated rather than ready for a long-term relationship. The first issue is that he is fickle. The ease with which he abandons Rosaline on first seeing Juliet is evidence that he is impulsive rather than mature in his decisions. A quotation to support this is:
Is Rosaline, whom thou didst love so dear,
So soon forsaken? young men's love then lies
Not truly in their hearts, but in their eyes (Act I, Scene 3, lines 66-69).
Since Romeo has spent most of the first act expressing a deep passion for another woman, it's hard to believe that we should take his instant switch in his affections at the sight of Juliet very seriously.
This quotation also supports the theory that Romeo seems to be mistaking lust for love. He is attracted mainly by outward appearances, as can be seen in his praise of Juliet's beauty:
The brightness of her cheek would shame those stars.
This does not seem like a solid basis for a lasting relationship.
Romeo's romantic gesture of climbing over the wall is actually another sign of his immaturity. He risks his own death and dishonoring Juliet by doing this, but rather than thinking about the effect of his actions on Juliet or their families, he says,
And what love can do that dares love attempt;
Therefore thy kinsmen are no let to me.
This shows he is very self-centered, thinking only of immediate gratification of lust rather than about how his actions will affect the people around him.