You cannot wield an unarmed strike, so this does not work
The Brace Maneuver states:
When a creature you can see moves into the reach you have with the melee weapon you're wielding, you can use your reaction to expend one superiority die and make one attack against the creature, using that weapon [...]
You cannot wield an unarmed strike. I come to this conclusion because the rules are written using natural language and if somebody told me they were wielding their head, foot, or hand, I would be very confused. However, there is a stronger argument to make:
Unarmed strikes are not weapons, so this does not work
Regardless of whether or not you can wield an unarmed strike, the feature requires a weapon at two different times and unarmed strikes are not weapons:
[...] Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). [...]
Because unarmed strikes are not themselves weapons, they cannot be used for the Brace Maneuver.