Pharmacists are normally not authorized to give immunizations to infants/toddlers under age 3 per federal guidelines, but are permitted to do them down to that age subject to stipulations in state law for certifications, etc.
Using the PREP Act (Public Readiness and Emergency Preparedness Act), HHS has periodically been updating rules for childhood vaccinations administered by pharmacists as a result of the current pandemic and its aftermath of a troubling drop in vaccinations for other childhood diseases, with the latest update done back in January 2022 - Tenth Amendment to Declaration Under the Public Readiness and Emergency Preparedness Act for Medical Countermeasures Against COVID-19 (PDF version here)
States then have authorities based on state law.
There is a good (although not completely up-to-date) interactive website from a pharmacist's association, that details the laws in every state - https://naspa.us/resource/pharmacist-authority-to-immunize/ (state legislation update from last year here that has most likely been superseded but not updated at the site)
Interestingly, when I was doing this post and listening to the radio, I actually heard a story where the PA legislature was looking at updating the waivers in current state law regarding pharmacists and vaccinations set to expire at the end of the month and it seems all hell has been breaking out between pediatricians and pharmacists. 
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