Is it safe to whiten my teeth while I'm breastfeeding?

Would delay it. Whitening products aren’t recommended for children under age 16, for women who are pregnant or breast-feeding.
Yes. The active ingredient in bleaching gels is hydrogen peroxide or a more stable form called carbamide peroxide. Both forms would not be dangerous to the baby. Another consideration would be gum sensitivity to the bleach with hormonal inflammation to these tissues. It may feel better to wait until you are not nursing.