I went through the Quickbooks online API documentation and it looks like I've to create an App in Developer Dashboard and then provide Terms and Conditions, privacy policy pages, Connect/ Disconnect URLs, etc. in order to to use it. I need to implement this feature for my own website and don't want to make it an App. Can't I simply make API calls from my website, without having to go through the hassle of creating an APP, go through verification process and all the details?
You have to make an app, yes.
You do not need to publish the app or make it available to anyone outside of yourself.
All an "app" is in this context is basically registering your email address with Intuit, so that you can get a set of OAuth keys to be able to authenticate. Nothing more. You can use dummy URLs for the privacy, terms and conditions, etc. URLs.
The "hassle" is as simple as just putting the a dummy URL in and registering your email address with Intuit so you can get credentials.