We know Mercury must have a large metal core because it has a high density?

True. Mercury's density is 5.427g/cm^3. This is based on simple inference of size and gravitational pull of spacecraft that have visited it.

Mercury’s density can be used to infer details of its inner structure. While the Earth’s high density results appreciably from gravitational compression, particularly at the core, Mercury is much smaller and its inner regions are not nearly as strongly compressed. Therefore, for it to have such a high density, its core must be large and rich in iron.