Step 1: Identify the diagnosis. The child has bluish-white spots in the mouth (Koplik's spots) followed by a skin rash. This clinical picture is characteristic of Measles (Rubeola).
Step 2: Identify the causative agent. Measles is caused by Measles morbillivirus (MeV), belonging to the family Paramyxoviridae, genus Morbillivirus.
Step 3: Identify the genome type. Measles morbillivirus is a single-stranded, negative-sense, enveloped, non-segmented RNA virus. The nucleocapsid has a helical symmetry and associates with the matrix protein (M) at the base of a double-layered lipid envelope. Therefore, the genome of the measles virus is that of an enveloped virus with single-stranded RNA.
Step 4: Eliminate distractors. Option B is incorrect because Paramyxoviruses are enveloped, not naked. Option C describes Reoviruses, which have double-stranded RNA. Option D is incorrect because the measles genome is single-stranded, not double-stranded.
Conclusion: The correct answer is Option A -- Enveloped virus with single-stranded RNA.