Stone foundations of Roman houses, painted wall plaster and coins have also been found.
Cowlin Construction, working for developers Simons Group, has put up posters on the sites boundary hoardings detailing any new finds.
Viewing holes have also been provided allowing the public to view any on-site activity.
Due to the potential archaeological sensitivities of the site, Cowlin has appointed Wessex Archaeology to ensure the development receives the specialist attention it needs.
Neil Holbrook, archaeology consultant to Simons Group, said: “During their initial excavation Wessex Archaeology uncovered the remains of a Roman child, not an uncommon find in a Roman town as bodies of children were often buried inside the settlement.
“Stone foundations of roman houses, painted wall plaster and coins have also been found.”
Andrew Pollett, Simons Group project director, said: “Dorchester’s archaeological heritage is extremely important to the projects team as well as the people of Dorchester.
“We hope the viewing hols provided by Cowlin Construction along with the archeologically posters will ensure everyone is kept up to date.”
The Charles Street site has an important Roman heritage and lies close to the southern edge of the Roman town, Durno-varia.
The row of trees along South Walks marks the line of reconstruction of the Roman town walls which was once close to the Roman public baths.
Construction on the first phase of the Charles Street development project began in June. It will provide new offices for West Dorset District Council and a library and an adult learning centre for Dorset County Council.
The first phase is due for completion in August 2012.
Once specialists have examined any finds they will be offered to Dorset Count Museum.
THE Romans arrived in the Dorchester area around 43AD and stormed Maiden Castle, which was then occupied by the Durotriges tribe.
They set up the settlement of Durnovaria nearby and had most of the local tribes under control by 70AD.
The town was enclosed by a series of walls, much of which can still be seen in present-day Dorchester.
It became a major market centre for the surrounding countryside as well as an important road junction and staging post.
The Roman appetite for the theatre was also catered for by converting Maumbury Rings, originally a pagan burial site, into an open-air theatre.
They also built aqueducts, baths and town houses, one of which has been preserved as an attraction in the county town.
The Romans withdrew from Britain in the 5th Century.