[filiadragongurl]

You have it backwards^_^; hajimemashite is what you say when you've never met a person and it's like saying "This is the first time meeting you" but of course in English we'd say something like "nice to meet you" (and we just know that it's meeting for the first time.) Doozo yoroshiku is literal meaning more like "I leave myself in your hands, take good care of me" and of course we'd never say that in English either... so "nice to meet you" is certainly acceptable in this situation.

Essentially, they have a different feel of meaning in Japanese, but we don't have similar greetings in English, so they both roughly translate to the same thing in this situation.

That clear it up a bit?