Although it will focus on the battles faced by writers Jimmy Perry and David Croft, it will also be full of humour.
"It's a bit of a journey for the two guys and there are lots of ups and downs," said producer, Brett Wilson.
"It was very hard for the writers to convince the BBC to commission the series in the first place.
"A comedy about members of the Home Guard during World War Two wasn't very appealing to them.
"But there will also be a lot of humour and we have some great actors involved, including John Sessions who is playing Arthur Lowe."
The drama is being shot entirely in Northern Ireland.
"We are using Northern Ireland crew - all the heads of department ... costume, make up, production, even the accountants are from Northern Ireland," said Mr Wilson.
Locations include Cultra Manor in County Down, Broadcasting House and the Ulster Reform Club in Belfast.
"It's all going really well," he added. "I have never worked here before, so I wasn't sure.
"But it's been fantastic and I would love to bring more productions to Northern Ireland."
Dad's Army was first broadcast in the late 1960s. The original series ran for nine years and included 90 episodes.
It followed the adventures of the Home Guard unit of fictional town, Walmington-on-Sea, during World War Two.
The television series looks set to attract a new generation of fans with the release in October of a movie based on the series.
At its peak, the Dad's Army series was watched by nearly 18m viewers.
A documentary-drama about the making of the Dad's Army television series will begin filming in Northern Ireland this month.