This somewhat depend on if you mean MQTT v3 or MQTT v5 (new version of the spec which can have a bunch more optional headers).
I'll answer based on a minimal v3 as that will give the default smallest size and should still be valid for MQTT 5 iirc (it might have an extra flags byte) when not using any of the extras.
First a MQTT packet is made up of 4 parts (only parts 1 & 2 are used for all packet types, but for publish you need all 4)
- A control header, this is a fixed size of 1 byte
- A length field, which can be between 1 and 4 bytes depending on the size of the payload. In this case it will should be another single byte. (The maximum packet size is 256MB)
- A variable length header, which can be any length as it contains the topic name.
- Since you have not specified a topic lets say you are publishing to the topic
foo which will be another 5 bytes (2 for the length, followed by 3 for the topic)
- It has 2 bytes at the end as a packet id
- Next the payload in this case
Hello World! which is 12 bytes (when UTF-8 encoded)
So that should add up to a total of
1 + 1 + 5 + 2 + 12 = 21 bytes (or a overhead of 9 bytes on top of the payload)
More details here: https://docs.solace.com/MQTT-311-Prtl-Conformance-Spec/MQTT%20Control%20Packets.htm#_Toc430864901
If you really meant MQTT-SN then you should be able to work it out from the spec (http://www.mqtt.org/new/wp-content/uploads/2009/06/MQTT-SN_spec_v1.2.pdf) but it can be less as you can pre-configure topics and just refer to them by number so the header gets even smaller.