To be a good child, you should go to bed early and wake up early.
Literal
Good child [to become-になる][for-には] early-sleep early-rise do [nominalizer-コト] [copula-です].
早寝早起き is a four-character compound meaning 'early to bed, early to rise' — quintessential child-rearing wisdom. コト in katakana (normally こと) gives it a slightly playful or stylized look. ~には signals purpose: 'in order to.'