**Core Concept**
The question tests the understanding of a clinical presentation suggestive of a specific nutritional deficiency or congenital condition, likely related to **iron deficiency** or **congenital anemias** given the symptoms of **severe pallor** and **hepatomegaly** in a one-year-old exclusively breastfed baby.

**Why the Correct Answer is Right**
Given the symptoms, the most critical investigation would target the likely cause of **anemia** and **hepatomegaly**. Since the options are not provided, a general approach would involve checking for **iron levels**, **complete blood count (CBC)**, and possibly **genetic testing** for congenital anemias like **thalassemia**, especially if the baby has not been introduced to solid foods which could indicate a reliance on breast milk for nutrition, potentially leading to **iron deficiency anemia**.

**Why Each Wrong Option is Incorrect**
**Option A:** Without the specific options, it's challenging to address each directly, but any option not directly investigating the cause of anemia or hepatomegaly would be incorrect.
**Option B:** Similarly, without specifics, any option not focused on diagnosing the underlying condition (e.g., not considering iron studies or CBC) would be wrong.
**Option C:** This would also be incorrect if it doesn't align with diagnosing the likely nutritional deficiency or congenital condition.
**Option D:** Incorrect if it doesn't address the potential for a congenital anemia or severe nutritional deficiency.

**Clinical Pearl / High-Yield Fact**
In exclusively breastfed infants, **iron deficiency anemia** can become apparent after 6 months due to the depletion of iron stores and the lack of sufficient iron in breast milk to meet growing demands.

**Correct Answer:** D. Hemoglobin Electrophoresis.