Keats characterizes the nightingale as being at "ease" and "too happy in thine happiness." He means to say that the nightingale is so at ease that it has no cares at all. This contrasts with the speaker himself who is burdened with melancholy. The nightingale is full of happiness because it is not burdened with the knowledge of growing old, mortality and death, and the passage of time. In other words, the speaker knows these things. He is aware of his own mortality and the fact that life is fleeting. The nightingale, on the other hand, is not aware of these things and is, therefore, full of happiness. In the third stanza, the speaker notes how the nightingale is not burdened with these thoughts:
Fade far away, dissolve, and quite forget
What thou among the leaves hast never known,
The weariness, the fever, and the fret,
Here where men sit and hear each other groan;
Where palsy shakes a few, sad, last grey hairs,
Where youth grows pale, and spectre-thin, and dies;
The speaker tries to at least forget the knowledge of his own mortality. He supposes that wine ("a draught of vintage") might allow him to forget this and be more like the carefree nightingale. But this simply dulls his melancholy, so he tries to escape his worries via his own poetry. Past generations have heard the nightingale's song and future generations will as well. The best the speaker can hope for is that future generations will hear/read his poetry. He has resigned himself to the fact that human experience is necessarily burdened with knowledge of life and death. He ascribes a kind of immortality to the nightingale (and more particularly to the nightingale's song). It is immortal because it is not aware of (or does not acknowledge) death and the passage of time.