Hi @Lydia
It depends what kind of residence permits you and your daughter have. If you have paragraph 25, section 1 or 2, then you are entitled to it.
If you have paragraph 25, section 3/4/5, then you are only entitled to it if you have been in Germany for at least 15 months.
The benefit is called 'Unterhaltsvorschuss'. What matters is not that the other parent is not in Germany, but whether the other parent is paying any financial support for the child.
In the application you are obliged to provide any information about the father's residence and contact details. The 'Unterhaltsvorschuss' is different to other benefits. It is an advance payment from the Jugendamt if a parent is not paying. THe Jugendamt then will try to regain this money from the other parent. It is for this reason that they will ask for his whereabouts and contacts details.
Best,
Éanna