Preamble
Without vowel markings the Hebrew word for "almond" and "watching" are the same, שקד. With the vowel markings, almond is שָׁקֵ֖ד (šā-qêḏ), and "watching" is שֹׁקֵ֥ד (šō-qêḏ). In the days prior to vowel markings, those who read the text would have had to have heard it read to them with the distinctive vowel sounds, otherwise the difference would have been lost over time.
The use of these two words could be a pun that Jeremiah's audience would have readily understood, but for us, many, many centuries from the time, the pun, if that's what it was, seems very obscure.
However ...
šā-qêḏ and šō-qêḏ
Moreover the word of the LORD came unto me, saying, Jeremiah, what seest thou? And I said, I see a rod of an almond šā-qêḏ tree. Then said the LORD unto me, Thou hast well seen: for I will hasten šō-qêḏ my word to perform it.
-- Jeremiah 1:11-12 (KJV)
A rod is used for discipline, which is how God intends to use it.
This particular rod, though, is an almond branch. Gesenius suggests the significance of the almond branch is connected to the fact that almond trees are the first to wake up after winter. They are "watching" trees, i.e. watching for the approach of spring. So, the branch will be a "watching" rod.
Okay, if šō-qêḏ means "watching", why has the KJV given "hasten". The only reason I can imagine is that the almond tree doesn't just watch for the signs of spring, it is eager for spring to hurry along. Gesenius also suggests there is a hurry-up sense to the word.
This idea will seem a little more plausible when the other uses of שֹׁקֵ֥ד (šō-qêḏ) in Jeremiah are investigated.
Other uses of šō-qêḏ
Wherefore a lion out of the forest shall slay them, and a wolf of the evenings shall spoil them, a leopard shall watch šō-qêḏ over their cities: every one that goeth out thence shall be torn in pieces: because their transgressions are many, and their backslidings are increased.
-- Jeremiah 5:6 (KJV)
Here שֹׁקֵ֥ד (šō-qêḏ) is used to depict a leopard watching and waiting for the gates to open, with the sense of hurry-up-and-open, so that when the people venture forth they can be pounced upon and torn to pieces.
Behold, I will watch šō-qêḏ over them for evil, and not for good: and all the men of Judah that are in the land of Egypt shall be consumed by the sword and by the famine, until there be an end of them.
-- Jeremiah 44:27 (KJV)
A group of people have defied God's instructions and run to Egypt for protection (Jeremiah 42,43), and God tells them through Jeremiah, that He will bring Egypt's enemies down upon them, and those who have no heart to return to Jerusalem will be consumed in the process.
In the past God had put a hedge around His people and has watched them for their good, but since they cared more for the things outside the hedge than they did for those within, the time had come for the hedge to go and for the heathen nations to have their day.
Nonetheless, God would see that a remnant from Egypt, whose hearts were fixed on Him, would return to Jerusalem (Jeremiah 44:28).
Conclusion
The "rod of an almond tree" is how Jeremiah depicts the enemies that God has allowed to descend upon Jerusalem and His people. Lions and wolves and leopards who have been watching and waiting and eager for God to remove His protective hand, so they can devour this insignificant little nation whose only claims to fame are what He has done for them.