Answer
The electric field of this system is nonzero. It would become zero only in the case that the two charges touch ($d=0$), neutralizing each other.
Work Step by Step
The electric field is the force per charge at a given location in space.
$\vec{\mathrm{E}}$ points in the direction of the force experienced by a positive test charge.
The electric field a distance $r$ from a point charge $q$ has a magnitude given by $\mathrm{E} =k\displaystyle \frac{|q|}{r^{2}}$
At any point in space surrounding these two charges, there are nonzero components of the electric field vector. At some points the components may cancel, but this is a special case, where fields point in opposite directions. In the general case, the components of the field act at angles to each other, so a net field vector exists.
The electric field of this system is nonzero. It would become zero only in the case that the two charges touch ($d=0$), neutralizing each other.
