What WordPress handles for pet services businesses
Online booking for appointments or stays. Booking plugins such as Amelia add services, times and booking forms; choosing a staff member is in its paid tiers.
Pet details before the first visit. A form plugin can collect the basic details before a first appointment; keep sensitive information in a secure system chosen for it, not a website form or email. Owner contact details and pet records are personal information. Keep them in your booking or practice system rather than an email inbox, and ask only what the first visit needs.
Areas you cover for mobile services. There is no core feature for this, so a suburb or postcode check is built as a small custom block.