Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
A one-year-old girl is not religiously responsible, and therefore, she is not required to wear hijab.
In his response to your question, Sheikh Muhammad Nur Abdullah, former President of the ISNA (Islamic Society of North America) and member of the Fiqh Council of North America, states,
Dawah should be practiced with wisdom and good admonition. Asking a one-year-old girl to wear hijab is an unfounded form of rigidity.
A one-year-old girl is not religiously responsible, and therefore, she is not required to wear hijab. It is only required at the age of puberty, meaning, when the girl begins to menstruate.
It is also advisable to start training your daughter a little bit before puberty in order to prepare her for it. By no means can we pressure a sister to put hijab on her one-year-old daughter; that is nothing short of extremism and lack of understanding of Islam.
Having said this, I advise all those sisters to practice dawah according to the way of the Prophet Muhammad (peace and blessings be upon him) who taught us to use wisdom, kindness and gentleness in our approach.
We should not pressure people, especially new Muslims, to do everything at once. We should try to attract people to Islam, rather than discourage them or make them run away from Islam.
Allah Almighty knows best.