I believe you are mostly right in what you say, but not exactly.
What you are talking about comes from the second scene of the second act. This is the famous balcony scene where Romeo talks to Juliet while she is on her balcony.
You are right in that they do exchange vows -- they swear that they love one another.
But they do not actually plan to get married the next day. Instead, they plan that Romeo will send word to Juliet to tell her what his plans are. If he is serious he is supposed to have her messenger come tell her when they will be married.
Romeo and Juliet exchanged vows and planned to get married the next day.