I just acquired a rental property. Can I use my existing program to separately track these finances?

One QBSE/QBO account is for one company file. You can manage branches/divisions by utilizing the Class/Location feature available in QBO Plus and Advanced. Otherwise you should open a new account.

https://quickbooks.grsm.io/US

https://quickbooks.grsm.io/us-promo

If you are using QBO to manage your property, explore this app to integrate with your QBO later.

https://home.tenantcloud.com/signup?affiliate=3jqxsies8ncnqqwj