Digitonomy,
Phemie’s statement is quite consistent with the canons and the liturgical texts. A priest must confirm if possible in such circumstances.
In a danger of death situation, the law gives any priest the faculty to administer confirmation (c. 883, 3º) . Further, a priest who has the faculty to confirm must use it in favor of those for whom it was given (c. 885 §2). Danger of death trumps the other times, such as the age of discretion or other age established etc., mentioned in canon 891.
The Rite of Confirmation (n. 11) states: "In this case every necessary precaution is to be taken to ensure that in the event of danger of death or serious problems of another kind children receive confirmation in good time, so that they are not left without the benefit of this sacrament.”
The Rite of Christian Initiation for the Dying says that a priest who baptizes should confer confirmation after baptism if the sacred chrism is at hand and there is time (n. 276). It also addresses care of a dying child at n. 280, and says “as far as possible, the rite of baptism for children and for children and the rite of confirmation are celebrated in the usual way.” Further, “a dying child with the use of reason shares the common responsibility of receiving viaticum.” It also is stated as desirable that an even younger child complete initiation by reception of the Eucharist, in accord with the practice of the Church. The rubrics of the Rite then say if confirmation does not take place, the neophyte should be anointed in the usual way.
The Rite of Baptism for Children permits a priest or deacon to use the shorter form (even “un”blessed water and the formula, etc) at the moment of death or when there is urgency because of imminent danger of death (21,1). It also says, “In danger of death, if there is time and he has the sacred chrism, the pastor or other priest enjoying the faculty should not fail to confer confirmation after baptism. In this case he omits the postbaptismal anointing with chrism.” (n. 22)
(As noted, this post baptismal anointing is quite different from the conferral of the sacrament of confirmation. According to the Rite of Baptism for Children, n. 18.3, the post baptismal anointing signifies the royal priesthood of the faithful and enrollment into the company of the people of God. But it is not the sealing with the Holy Spirit in the Sacrament of Confirmation.)
A priest would have to prudently judge the "as far as possible"or “if there is time” parts and would have to have sacred chrism. (Remember, a priest may bless the oil of anointing the sick in a case of necessity but only a bishop can consecrate sacred chrism. So a priest cannot “whip up a batch.”)
But circumstances can vary on all accounts, and things can move quickly.