Step 1: Start from the mechanism. Dactylitis in this context is a vaso-occlusive event, so look for the disease that physically blocks small-bone blood vessels.
Step 2: Among the options, only sickle cell anaemia produces rigid, sickle-shaped erythrocytes that jam the marrow microcirculation of the metacarpals, metatarsals, and phalanges, causing infarction.
Step 3: Clinically this shows as a tender, swollen hand and foot, classically the earliest presenting feature of sickle cell disease in babies.
Step 4: Rule out the rest: $\text{haemophilia}$ and von Willebrand disease are clotting-factor deficiencies giving bleeding into joints, not vaso-occlusion; measles is a paramyxovirus rash illness with no bone-pain syndrome.
Step 5: Hence the answer is sickle cell anaemia.\[\boxed{\text{Sickle Cell Anemia}}\]