The grieving father of an eight-year-old boy allegedly murdered by his mother in a home on Victoria's Mornington Peninsula has expressed his "emptiness".

"I feel empty, still in shock. I have lost the best part of me," Lee Moran, who lives in China, posted on Facebook.

"Words cannot describe how much I love and miss my little fella."

Mother Joanne Finch faced the Melbourne Magistrates’ Court today showing little emotion after Brodie Moran was found dead inside a home.

Less than a day ago, the 41-year-old was arrested after emergency services were called to their Tootgarook home and the boy was found dead.

Ms Finch was last night charged with one count of murder in an out-of-sessions court hearing.

This morning locals paid tribute to Brodie, who has been described as a "happy child".

The local community has been rocked by the death, with many people arriving to lay flowers for the Year 2 student.

Police are investigating whether Brodie may have been suffocated.

The court heard today Ms Finch is on anti-depressant medication.

She was remanded in custody until June 29.

Tootgarook Primary School, where Brodie attended, issued a statement from the principal, calling the death a "tragic event".

"Support is being made available through the school for friends, classmates, students, staff and anyone else in our school community who may need it during this difficult time," Principal Wayne Whitworth said. 

Locals said Brodie lived at the home with his mother and a man.

Police said the man is not a person of interest in the case.

One neighbour said they had seen the boy playing on the trampoline that sits in the home's front yard.

"He was always a happy child," the neighbour said.

"We'd wave hello as we were collecting the bins. They'd always say hello back."

"It's absolutely tragic, I'm gutted," another neighbour said.

Just before 8pm yesterday, two women arrived at the home to leave flowers in tribute to the boy.

"We're just paying our respects to a beautiful eight-year-old child," one of the women told 9NEWS.

The home was up for sale at the time of Brodie's death, and was due to be open for inspection this weekend.

Neighbours said the family had been renting the property for about a year.

Anyone with information is urged to contact Crime Stoppers on 1800 333 000.

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