I think it would be a great trip. monsoon will not bother you. in Andman temperature is average around the year same. in seven days, you can visit most of the places like port Blair city, Havelock and Neil Islands, north bay and Ross island, baratang jungle and mangroves, mount harriat. hotels are easily available at City or near airport. for convenience, book them advance. for hiring a car, you can ask the hotelier, they will manage. and believe me there is no extra cost charging for that. my Andman self arrange tour article is here if you want to visit. otherwise msg me I'll happy to help you.
HI Sudeep, Andaman during September will be good. You can expect some rain but that should not affect your trip. It is a beach lover's paradise. I visited Andaman in June end and it was one of the best trips. You can refer this for the places to visit, itinerary, things to keep in mind, how to plan etc. https://www.soulandfuel.com/post/explore-andaman-in-5-days PS : Scuba diving in Havelock is something you should not miss.