The transfer on the serial port will take time. As soon as the transmitting side is done with one character, it will be able to start sending the next.

The only time you need to add own delays is if you run with a high baudrate, and the receiving side isn't fast enough to extract and process the data as fast as the baudrate allows. With 9600 baud, your receiver must be able to extract and process about 1000 characters/second. If the receiving side doesn't have a FIFO, then it will not be enough that the average speed of the receiver is good enough. It must always manage to pick up the next character within one full character time, or the UART will get an overrun error - fully receiving a new character before the previous character was read out.

In some situations, delays may also be used for framing, i.e. a long delay between two characters are used to indicate the start of a new message, while multiple characters received with a very short gap (relative to the baudrate) will be considered part of the same message.