The eminent Muslim scholar and renowned Da`iyah, Sheikh `Abdel Khaliq Hasan Ash-Shareef, stated that

A female cousin can perform Hajj on behalf of her deceased father (may Allah have mercy on him and grant him Paradise) who is a relative to her. Also, her doing `umrah on his behalf is acceptable and he will be rewarded for that and she will gain a similar reward without reducing her father’s reward.