The description of Dual Wielder says that you
Gain a +1 bonus to AC
Use Two-Weapon fighting, even when the one handed melee weapons you are using aren't light.
You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one.
pg 165 PHB
The description for Two-Weapon Fighting says
When you attack with a light melee weapon you're holding in one hand, you can use a bonus action to attack with a different light weapon that you're holding in the other hand. You don't add your ability modifier to the damage of the bonus attack unless the modifier is negative.
pg 195 PHB
The description of Bonus Actions says:
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available pg. 189 PHB
And the Martial Arts Description states:
When you use the Attack action with an unarmed strike or a monk weapon on your turn, you can make one unarmed strike as a bonus action.
The upshot is that you get the +1 to AC as stated above. Any character can attack with two unarmed attacks provided the second attack is the bonus action. What a monk gets is to add their ability modifier bonus to damage with the second attack. No other player gets that.
But, Dual Wielder is redundant and unneeded. If you put the 2 points it would cost you for the feat into Dexterity or Wisdom you would an extra point of AC, plus whatever bonuses apply to your skills.