**Core Concept**
The question is testing the understanding of the mechanism of toxin production in Corynebacterium diphtheriae, a nonspore-forming, gram-positive bacillus. This bacterium can produce diphtheria toxin when it is infected with a specific bacteriophage that carries the toxin gene.

**Why the Correct Answer is Right**
The correct answer is related to lysogenic conversion, a process where a bacteriophage integrates its genetic material into the host bacterium's genome, conferring new traits. In this case, the bacteriophage carries the gene for diphtheria toxin, which is then expressed by the host bacterium. This process is known as lysogenic conversion and is a key mechanism by which C. diphtheriae becomes toxigenic. The toxin gene is encoded on the bacteriophage, and its integration into the bacterial genome leads to the production of diphtheria toxin.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option may suggest that the bacteriophage encodes the toxin gene, but it does not explain how the bacteriophage integrates into the host bacterium's genome, leading to lysogenic conversion.
* **Option B:** This option may imply that the bacteriophage is responsible for toxigenicity, but it does not provide a clear mechanism for how the bacteriophage confers toxin production on the host bacterium.
* **Option D:** This option may suggest that the DTaP vaccine is responsible for toxigenicity, but it is actually the lack of vaccination that makes the child susceptible to infection with a toxigenic strain.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that lysogenic conversion is a key mechanism by which bacteria become toxigenic, and it is often mediated by bacteriophages that carry genes for toxins. This concept is critical in understanding the pathogenesis of diseases caused by toxin-producing bacteria.

**Correct Answer:** C.