What is the procedure of Antim Sanskar when a unmarried women dies? Does she dress like a bride? Who gives the agni to her pyre?
The title of your question is asking for unmarried girls. And my answer is for that query.
If you are asking about married ladies then your question is an exact duplicate of :Who should do Antim Sanskar (funeral rites) of married woman?
For Unmarried girls:
According to Baudhayana such women should NOT be cremated. But at the same time it also says that some people do perform last rites for such women.
See the following verses:
Among people belonging to the same ancestry, the relationship based on common ancestry extends to the seventh generation. 3
Only a bath is prescribed when a child dies before it is seven months old or before teething. 4 When a child dies before it is 3 years old or before teething, no offerings of food or water are prescribed, and it should not be cremated.
5 The same is true when unmarried girls die.
6 Some do perform these rites for married women, 7but they do it just to curry favour with people; ritual formulas are thought not to apply to women.
Baudhayana Dharma Sutras 18.104.22.168-7
And, should not be cremated means they have to be buried.
For married women:
Having cremated a becoming wife, dead before, with the fire of the vessel, one should get himself re-married without delay [and consecrate the Fire again]. (5)
A twice-born person, who is conversant with religious laws, should cremate a good-charactered wife of the same caste, who dies before, with the sacrificial vessel according to the Agnihotra- method. (6)
One who, having his first wife living, cremates the second wife with the Vaitanika is equal to the destroyer of a Brahmana. (7)
Katyayana Smriti Chapter 20
So, for married ladies their husbands should do the final rites. In husband's absence it is the sons who should do it.