If I'm nursing my baby, can I still take this azithromycin tablet?

Yes. Since low levels of Azithromycin is secreted into breast milk it is unlikely to cause adverse effects in breastfed infants. Monitor the baby for possible side effects, such as diarrhea, thrush and diaper rash.
General rule. When it comes to breast feeding and antibiotics there is a general rule. If the med is considered safe enough to give the infant at that age it is fine for you to take while breastfeeding. This applies to this med. If the need arises in the future, simply let the doc know you are BF and they can select one safe for the infant.