That same order has instructions for children, although not concise:
Source:
https://www.cdc.gov/quarantine/cruise/pdf/Vax-Order-10-30-21-p.pdf
QUOTE
Children. The Proclamation excepts noncitizens who are
nonimmigrants for whom, given their age, requiring
vaccination would be inappropriate, as determined by the CDC,
taking into account global vaccine availability for
individuals in that age group. In the United States, COVID-
19 vaccinations are widely available for adolescents, with a
vaccine approved for those 16 years and older and authorized
for those 12 to 15 years of age. However, the same
availability does not exist globally. Accordingly,
considering the difficulty potentially posed to families
traveling together when some members of the family can be
vaccinated and others cannot, persons under the age of 18
years meet the age-based exception in the Proclamation.
Noncitizens who are nonimmigrants and who are under the age
of 18 years and unable to present
Proof of Being Fully
Vaccinated Against COVID-19 must present a completed
Covered
Individual Attestation to the airline or aircraft operator
prior to embarking an aircraft destined to the United States.
However, as part of this attestation, children under the age
of 18 will not be required to attest (or have a parent or
guardian attest on their behalf) to having arranged to self-
quarantine in the United States after arrival. Based on the
potential difficulty that self-quarantine may pose to
children under 18 years of age especially when accompanied by
a vaccinated parent or guardian who is not required to self-
quarantine, CDC has determined that self-quarantine should
not be required. Nevertheless, children under 18 years of age
will be required to attest (or have a parent or guardian
attest on their behalf) to arranging to be tested for COVID-
19 3-5 days after arrival and to self-isolate if the test
result should be positive or if the child develops COVID-19
symptoms. CDC believes that this approach fairly balances the
interests of families traveling to the United States with
protecting the public’s health. CDC guidance strongly
recommends vaccination for all eligible children under 18.
However, given the still evolving circumstances of
vaccination for children, attestation regarding post-arrival
vaccination will also not be required for children under 18
at this time. This determination will be periodically
reevaluated.
END QUOTE
