Yes, the customer details and booking history you build up on your portal belong to your business, and you should be able to take them with you if you ever move on. Your portal is your shop front, so the enquiries, the passenger records and the past bookings that sit behind it are your own trading records.
In practice this usually means an export in a plain spreadsheet format covering your customers, your bookings and your invoices, which you can open in any ordinary office program or load into another system later. Some of the finer detail is harder to carry across, for example supplier reference numbers or documents that were issued by the airline or the hotel, because those live in the supplier system rather than in your portal. Anything held in your own payment gateway or your own email account stays with you either way.
How much notice you need to give, and whether the export is included in your plan or arranged separately, does depend on the plan you are on and on the terms you agreed at the start, so it is worth reading that part rather than assuming. It is also fair to ask what happens to the records after you leave and how long they are kept.
The simplest thing to do next is to ask for a sample export while you are still trading normally, so you can see exactly what the file contains and check that it holds everything you, your team and your accountant would need.