1) "I'm looking forward to meeting you."
2) "I look forward to meeting you."
I tried to imagine how the sentence could be grammatically correct without using the gerund suffix on the word 'meet,' and the only thing I could come up with was this:
3) "I can't wait to meet you."
By the way, your first sentence ends as an interrogative, so it should have a question mark. Secondly, you incorrectly included a space between the word 'you' and its punctuation; the closing quotation mark. You repeated the same mistake with the word 'correct,' and with the word 'me'.
In English, there is no space between the last character in a sentence and the punctuation.