What you wrote is okay, but the original emphasizes that he’s sort of settling. He’d rather be a prince, but can’t, so he figures seeing one is the next best thing. 就 is a hard word to explain in simple terms as it has so many usages and no real direct English equilalent, but you could likely translate it here as “just”.
As for the 已经, we do something pretty similar in English. It highlights the fact that seeing a prince is something he already can do. Compare:
Seeing a prince is pretty good
Just seeing a prince is already pretty good.
Both are fine, but the second one reads like you’re trying to comfort yourself rather than simply making a statement.