There are two options when it comes to allowing customers to add/edit their pets vaccination dates when using the online booking portal.
Option 1
Allow them to just upload a copy of their vaccination cert via the document upload feature on the online system. From the online booking portal settings page you need to enable the 'Allow Customers to view and upload documents'. Once enabled customers can upload their vaccination certs, when they do you will be sent an email notification - so you can review the document and add the dates to the pets record.
Options 2
You can allow the customer to add in the dates for their vaccination records directly against the pets record. From the online booking portal settings page you need to enable the 'Allow Customers to add/alter vaccination dates online', once enabled when customers go to add a booking they will see the vaccination dates for their pets and can add/alter them as necessary.