To go begging means to be available for one to take or claim, and in this sentence it is suggesting that laoghaire be available to take or claim a gaberlunzie badge.
Consider the staetement "I didn't bother suggesting that we allow laoghaire to put in for a gaberlunzie badge and to be available for one to take or claim through the parish.". Based on this statement, is "I didn't bother suggesting that we allow laoghaire to put in for a gaberlunzie badge and go begging through the parish." a true statement? Yes/no/unknown