I am doing my postgraduate in engineering. What is the process of publication of my paper on Q1 journals? How long it will take to publish?

Well, Publishing a Q1 paper is time-consuming. You have to be patient enough.

If you want the paper reputably published, e.g. with peer reviews, then it's going to take a minimum of ~ 1/2 year. You submit your paper before a review deadline. The papers are reviewed over the course of a few months. If your paper is accepted, you make some recommended corrections and re-submit. A few months later the conference happens and your paper is published in the proceedings.

If you want to be published in journal articles or as a book chapter, the wait is typically longer, often years.

You can check this one also-

https://theconferencealerts.com/discuss/channels/how-to/how-to-get-published-in-high-impact-journals-an-essential-guide-11

Thanks for your help.