Is it permissible for us—even though we are daughters and capable—to collect the price of the the sacrificial animal (Udhiyah) and offer the sacrifice, knowing that my father does not offer the sacrifice?

The father should not neglect the sacrifice (Udhiyah (definition)) if he is able to perform it, as it is a confirmed Sunnah (definition). His single sacrifice suffices for him and his household. It is permissible for daughters to offer a sacrifice on behalf of themselves by sharing in a camel or a cow, provided that each of them has at least one-seventh of it, by analogy with the Hady (sacrificial animal offered during Hajj). It is not valid to share the price of a single sheep, but it is valid to share in the reward and sufficiency if one of them pays the full price and includes her sisters, provided that they live in the same dwelling and the expenses are shared from it.