Do you think that I could make my daughter video chat with her cousins?
Are you worried about how her experience will be?
She is well protected by her privacy
If your daughter doesn't want to video chat with her cousins, you shouldn't force her to. She should be able to do what she wants within reason.
Her cousins have allowed this.
Well you should ask her if she wants to, and if she says yes then the video chatting sounds fine. If she says no, however, then you should respect what your daughter wants and not push her or else she may grow up to resent you.