ANSWER:
No. This is not permissible as ruqya should be done on someone who is present.
His parents can recite the duas of protection.
PROTECTION FOR CHILDREN
If you say this Duaa in the morning and evening, this would would protect you and your children with the grace of Allah.
Allahumma inni as’alukal- afiyata fid-dunia wal-akhirati.Allahumma inni as’alukal-‘afwa wal afiyata fi dini wa dunyaya,wa ahli wa maali.Allahumma-ustur ‘awrati wa amin raw’ati.Allahumma-ihfazni min bayni yadaiya wa min khalfi,wa ‘an yamini wa ‘an shimali,wa min fawqi,wa a’uthu bi’athamatika an ughtala min tahti.
O Allah, I ask You for pardon and well-being in this life and the next. O Allah, I ask You for pardon and well-being in my religious and worldly affairs, and my family and my wealth. O Allah, veil my weaknesses and set at ease my dismay. O Allah, preserve me from the front and from behind and on my right and on my left and from above, and I seek refuge in Your greatness from receiving unexpected harm from below me [being swallowed up by the earth]).”
اللّهُـمَّ إِنِّـي أسْـأَلُـكَ العـافِـيةَ في الدُّنْـيا وَالآخِـرَة ، اللّهُـمَّ إِنِّـي أسْـأَلُـكَ العَـفْوَ وَالعـافِـيةَ في ديني وَدُنْـيايَ وَأهْـلي وَمالـي ، اللّهُـمَّ اسْتُـرْ عـوْراتي وَآمِـنْ رَوْعاتـي ، اللّهُـمَّ احْفَظْـني مِن بَـينِ يَدَيَّ وَمِن خَلْفـي وَعَن يَمـيني وَعَن شِمـالي ، وَمِن فَوْقـي ، وَأَعـوذُ بِعَظَمَـتِكَ أَن أُغْـتالَ مِن تَحْتـي
The Prophet (blessings and peace of Allah be upon him) used to seek refuge with Allah for al-Hasan and al-Husayn, and he said: “Your father (Ibraaheem) used to seek refuge with (these words) for Ismaa’eel and Ishaaq: A’oodhu bi kalimaat Illaahi’t-taammah min kulli shaytaanin wa haammah wa min kulli ‘aynin laammah (I seek refuge in the perfect words of Allaah from every devil and every vermin, and from every bad eye)”.