Remember that all potentials work by looking at how they vary from place to place-- absolute values at a given place are never of any physical importance. So when we take zero at the center, it's just a convenient convention.
Alright... That's somewhat counter-intuitive for me.
So does that mean that if I move a charge from infinity to the middle of the two opposite charges, no net work would be done?
That is also true-- it means that if we set the potential at infinity to be zero, that's the same convention as setting it to be zero at the center. You can tell that has to be true from the symmetry--if the charges are equal and opposite, what is going to be the sign of the potential at the center, relative to infinity? Which sign could possibly be singled out?
Shouldn't it have the exact same value as the potential at infinity?
Yes, by symmetry-- if it were to deviate from the value at infinity, the deviation would need a sign, and we should be able to reverse that sign by reversing the sign of the charges, but such a reversal is just a left/right reflection.