From what age must a girl begin dressing modesty?
Some Poskim rule that starting from age three, a girl is required to dress modestly, and it is thus forbidden for a man to Daven or learn Torah in her presence from age three and onwards, if she is not modestly dressed. Other Poskim however rule the necessity of dressing modestly and the prohibition of learning Torah and Davening in her presence does not begin at age three but rather at a later age, when the girl’s body is developed enough to cause men to have attraction to them [i.e. age 6-7]. Nevertheless, even in their opinion, it is proper to educate a girl to dress modestly from age three. Practically, the Rebbe concludes like the former opinion that according to Halacha girls must be educated from age three in the laws of modesty.
 So rule regarding a man praying or learning in presence of a three year old girl who is not modestly dressed: Biur Halacha 75/1 “Tefach Megula” in name of Shulchan Shlomo; Ketzos Hashulchan Vol 1, Haaros Page 90 in name of Chayeh Adam [that from 3 years old a girl is considered an Ervah regarding Shema and Torah learning]; Shut Daas Sofer 1/11; Ben Ish Chaiy Bo 8 brought in Kaf Hachaim 75/10 [concludes to be stringent when possible]; Halichos Shlomo 20/9 in name of Rav SZ”A; Az Nidbaru 13/1; Likkutei Sichos [18 p 448] and other prominent Rabbis of this generation; See letter of Rav Farkash in “The Jewel of our Crown” page 79; Chesed Lealafim 75/8, brought in Kaf Hachaim 75/10, leaves this matter in question regarding any Ketana; Ashel Avraham of Butchach 75 brings sides to be stringent and lenient in this matter. See Piskeiy Teshuvos 75/8 footnote 82aa
 So rule regarding a man praying in view of a young girl not properly dressed: Yifei Laleiv 75/2 [brings up question and leans to be lenient]; Maharam Brisk 2/70; Chelek Levi 36; Salmas Chaim 76; The Chazon Ish [16/9] famously ruled that the laws of modesty for a girl do not begin from age 3 but rather from a later age from when their bodies are developed enough to cause men to have desire for them; Chesed Lealafim 75/8, brought in Kaf Hachaim 75/10, leaves this matter in question regarding any Ketana; Ashel Avraham of Butchach 75 brings sides to be stringent and lenient in this matter. See Piskeiy Teshuvos 75/8 footnote 81;
 See Az Nidbaru 12/49; Or Letziyon 2/6-12; Piskeiy Teshuvos 75/8 footnote 87
 Salmas Chaim 67; Orchos Rabbeinu 2/204 that this applies even according to Chazon Ish ibid
 The Rebbe in a letter in Likutei Sichos [18 p 448] writes that according to Shulchan Aruch the age of Tznius needs to begin at three years old and a day, although one should not be oppressive about this and should speak in a pleasant way. [For a translation of the letter see “Beautiful within” page 39]