The Waples are heavily involved in the C3 Church at Frankton, outside Queenstown, where Mrs Waples is a pastor.
Mr Waples, originally from Southland, works as a builder in the area.
"We would like to thank the police, Coastguard and St John Ambulance as well as our neighbours and community for their amazing response," said the Waples.
"We are surrounded with family and friends and are blown away by the love that is being sent our way from near and far. Thank you for your prayers."
Queenstown police completed a scene examination today and will now file a report for the coroner.
"All parents know that they are vulnerable. It's the sort of thing that when the planets don't line up and things go wrong, it is every parent's worst nightmare," said local senior sergeant, John Fookes.
Funeral arrangements have not yet been confirmed.
Mr Fookes said the child had been inside the house, described as an older property which was "partially fenced", when her mother noticed her missing.
Police had come to the conclusion the child had walked through a gap in the fencing towards the lake, Mr Fookes said.
Officers searched along the foreshore at the Kelvin Heights Golf Course end of the walking track, which borders the lake.
"At around 12.45pm, police located the child face down in Lake Wakatipu, about 100m from where she'd last been seen," Mr Fookes said.
St John staff in Queenstown were called by police to assist at the scene.
"In spite of the best attempts at CPR by both police and St John Ambulance, the child did not regain consciousness," Mr Fookes said.
"There are a number of private jetties and shoreline vegetation such as trees and shrubs in the vicinity of where the child was found.
"They [the family] are naturally very, very upset and being supported by family, friends and Victim Support."
