Austen Harrison suffered fatal head injuries at the Hugo Boss shop in Bicester, Oxfordshire, in June 2013.
Hugo Boss UK pleaded guilty to breaching the Health and Safety at Work Act and Management of Health and Safety at Work regulations.
Sentencing is due to take place at Oxford Crown Court on 19 June.
Austen, of Crawley, West Sussex, had been playing with the unfixed steel-framed fitting-room mirror which toppled on to him while his father tried on a suit in the shop at the Bicester outlet village.
He underwent an emergency operation to relieve pressure on his brain but died four days later in hospital after life-support was switched off.
At a hearing at Banbury Magistrates Court on Tuesday, Barry Berlin, prosecuting on behalf of Cherwell District Council, requested the case should be sentenced at Oxford Crown Court where fines of Â£100,000 or more could be imposed, rather than the Â£20,000 possible at a magistrates court.
An inquest jury at Oxford Coroner's Court earlier this year returned a narrative verdict.
Austen's death was an "accident waiting to happen", the coroner said.
A designer store has admitted health and safety offences following the death of a four-year-old boy who was crushed when a 120kg mirror fell on him.