When children are exposed to any activity or sport they tend to develop interest (especially at her age). It may or may not be a passing interest, but I think (at least for now) it's a great way for her to have something she can share with her father.
She may find golf is something she'll always enjoy, or she may lose interest at some point. At the same time, she may become a pro. As long as she's interested in it I'd go with it. If, at some point, it seems to start to "take over her life" while she's still a child, some careful judgments may have to be made.
In the meantime, I'd just go with it. It's a nice thing. Kids enjoy, and benefit from, the chance to become involved with different activities. Sometimes parents' fear of "pushing" their children results in their denying kids' the chance to take part in constructive activities. Caring, cautious, parents generally know when their child's interest is his own and when it isn't.