The short answer
Yes. A new owner can register themselves and their pet and book a first consultation in one go, from a phone, without ringing you. Vetstoria, ezyVet, Provet Cloud and Covetrus all offer client facing online booking that creates or matches the client record, captures the pet, sets the appointment type and vet, and lands the slot in the practice diary.
What stops it happening is almost never the software. It is that the practice has not decided what a new client is allowed to book.
Decide that first
Before anyone touches a widget, answer four questions.
Which appointment types are open to a new client, and which are not. Most practices open a standard consultation and a vaccination appointment, and keep dentals, surgery and complex cases behind a request.
Whether a new registration books straight into the diary or arrives as a request the desk confirms. Straight in fills more slots. Requests give you control. Either is defensible, but the website has to say which one it is.
How much you ask for before the booking completes, and how much you collect afterwards.
Whether a previous practice's history is needed before the appointment, and who chases it.
The registration fields that matter
Required at booking: owner name, phone, email, postcode, pet name, species, breed, rough age and the reason for the visit. That fits on a phone screen and it is enough to open a record.
Requested in the confirmation, where the owner is at home and not mid decision: the previous practice and their permission to request history, insurance details, microchip number, current medication, and whether the animal has any handling notes your team should know before it comes through the door.
The temptation is to move all of that into the booking form because it saves the desk five minutes. Every extra required field costs completed bookings, and a booking you never received cannot be tidied up later.
Registration without a booking needs its own route
Some owners want to join the practice now and book later, usually because they have just moved. Give them a Register page of their own with a short form, and give people who already know what they need a Book button that skips it.
Both routes should exist in the header. Register and Book are different jobs and one button cannot do both.
What the site has to explain around it
The booking widget answers when. The website has to answer everything else, before the owner commits.
Whether registration is free. What the consultation fee is. What happens at a first appointment and how long it takes. Whether you need to request history from the old practice. What to do if the animal is unwell right now rather than in two weeks, which is your emergency route rather than the booking flow. And what your health plan covers, because a new registration is the best moment you will ever get to explain it.
Data, plainly
You are collecting personal data about the owner as well as records about the animal, so it lives in the practice management system, not in an inbox and not in a spreadsheet. Your privacy notice should say what is collected, where it is held and how long for.
Marketing consent is separate from the booking. A reminder for an appointment the owner made is a different thing from a newsletter, and consent for the second should be its own optional tick. Rules differ by country, so treat this as orientation and confirm what applies where you practise.
Test it as a stranger would
Once it is live, book yourself in as a new client from your own phone, including from an Instagram or Facebook in app browser, which is where a surprising share of pet owners arrive from. Complete the whole route: pick the appointment type, register the pet, submit, receive the confirmation, then cancel it and check the cancellation reaches the diary.
Repeat monthly. Booking products update their flows, and you would rather find a broken step yourself.
Where this sits
Registration and booking in a single flow, wired to the practice management system you already run, is the core of every veterinary clinic website we build, and the same pattern runs across our other pet business websites. Our packages are on pricing. The software can do it. The decision about what a new client may book is the part that needs you.