ESV - 19 And he took bread, and when he had given thanks, he broke it and gave it to them, saying, "This is my body, which is given for you. Do this in remembrance of me.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Baptism is ideally one of the first acts of a believer, so would normally come first before communion. However, there is no "have to."
When I was little, I was considered 'too young' to be baptized yet even though I had been a professing Christian for years. The church group also had a rule that one was not to partake of communion unless they were baptized. Both of these 'rules' were nowhere to be found in scripture.
While I was not 'allowed' to get baptized until I was nine, I did get to take communion a few times with parents or at events or with other groups which was very meaningful for me, as it is one thing Jesus asks us specifically to do in remembrance of Him.