All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
No doubt that having a child and good health are among the precious and greatest Blessings of Allah. Every person should be grateful to Allah for His utmost and innumerable Blessings.
We do not know any particular form of worship to show gratitude to Allah for a particular favor except the prostration of thankfulness to Him. The Prophet and his companions used to perform that prostration when they received a bounty or were rescued from some trial. Imaam Ahmad narrated in Al-Musnad from Abu Bakr that when the Prophet received something which pleased him or some glad tidings, he would perform a prostration in thanks to Allah.
Imam Al-Bayhaqi reported with a chain that meets Al-Bukhari's conditions, that when 'Ali wrote to the Messenger of Allah, informing him that Hamadhan (an Arab tribe) had embraced Islam, the Prophet prostrated, and when he raised his head, he said: “Peace be upon Hamadhan.”
The one who has been granted a child should, first of all, offer Aqeeqah; i.e., to sacrifice a sheep for a baby girl and two sheep for a baby boy, shave the child’s head, and give silver equal to the weight of the baby's hair in charity.
A Muslim is also obliged to raise his child according to the Sharee’ah, teaching him Islamic conduct and morals. When he reaches the stage of discrimination (that is seven years), he should also be taught the rulings of performing the prayer since at this age a child is ordered to perform the prayer. If a child is able to learn before seven, then he may be taught earlier.
Allah knows best.