Yes, in most cases you can link your travel agency software to your accounting system so a booking only has to be entered once, although how smoothly it works depends on which accounting package you use and what your plan includes.
The usual arrangement is that every confirmed booking creates a record holding the supplier cost, the selling price, your markup and any tax, and that record is passed across to your accounts as a sales invoice with a matching supplier bill. Some packages have a ready made connection that sends this over as soon as the booking is made. Where there is no ready made connection, you can normally export the same information as a file on a regular schedule and import it, which still saves your team from typing anything twice.
It is worth being clear about the limits before you plan around this. Not every accounting package can be connected directly, so that is something to confirm for the one you use. Cancellations, amendments and refunds usually need a credit note rather than a simple correction, and if you sell in more than one currency you will want to agree which exchange rate is used, so that your accounts and your booking reports do not slowly drift apart from each other.
The next step is to tell us which accounting package you use and who looks after your books, so we can check whether a direct connection already exists for it or whether a scheduled export is the better fit for the way you work.