Step 1: Interpret the key findings.
A one-month-old infant with epiphora (watering/tearing) and an enlarged corneal diameter points toward elevated intraocular pressure (IOP) causing distension of the immature, elastic sclera and cornea. The classic triad of primary congenital glaucoma is: epiphora, photophobia, and blepharospasm.
Step 2: Define Buphthalmos.
Buphthalmos (Greek: "ox eye") refers to the enlargement of the entire globe secondary to raised IOP in infancy. Because the neonatal sclera is distensible (unlike the rigid adult sclera), elevated IOP causes the whole eye to expand. This results in an enlarged corneal diameter (>12 mm at birth is suspicious; >13 mm is diagnostic), corneal oedema, and Haab's striae (horizontal breaks in Descemet's membrane from stretching).
Step 3: Differentiate from other options.
Hurler's syndrome can cause corneal clouding due to mucopolysaccharide deposition but does not cause epiphora or globe enlargement as the primary feature. Galactosemia causes early-onset cataracts due to accumulation of galactitol but does not cause epiphora or buphthalmos. Cataract presents with leukocoria, not epiphora or enlarged corneal size.
Conclusion: The correct answer is Buphthalmos (primary congenital glaucoma).