The HTTP part of the packets is relatively easy. Just put the HTTP request in the payload. The hard part is doing TCP. This requires sending the packets to initiate the connection, and handling all the details of windows, flow control. Servers are not going to accept HTTP requests that don't come as part of a valid TCP connection.

Code to do this is already written. It is in the operating system in the network stack. For TCP protocols, making a normal connection is the way to go.

You could reimplement TCP/IP in Perl. That would be cool, but is a lot of work. You will need to learn a lot of networking to do it.