Jamaica is set to loosen colonial ties with Britain by moving to replace the Queen as head of state with a president, the country's new prime minister has indicated.

Nearly fifty years after independence, Portia Simpson Miller, a charismatic populist who won a landslide election victory last week, said Jamaica would move to cut links with the monarchy and become a republic.

"I love the Queen. She's a beautiful lady," Simpson Miller told 10,000 guests on Thursday at the residence of Jamaica's governor-general, the Queen's representative on the island. Switching to patois, she added: "But I think time come."

The move reflects an accelerating drift towards republicanism among Commonwealth Caribbean countries. Guyana and Trinidad and Tobago have both dropped the Queen as head of state, while opting to remain in the Commonwealth.

Capital punishment is another bone of contention for Jamaica, which has one of the world's highest murder rates, with violent crime a daily occurrence. The judicial committee of the privy council (JCPC) – the London-based highest court of appeal under the current constitution – has repeatedly blocked attempts to enforce the death penalty, a move seen as colonial-style foreign meddling.

This week Simpson Miller vowed to introduce reforms to make the Caribbean court of justice the final appeal court in all criminal matters. The move would repatriate Jamaica's sovereignty fully, she said.

On 29 December the 66-year-old led her centre-left People's National Party (PNP) to a landslide win over the centre-right Jamaica Labour Party, winning 42 of 63 seats.

The victory was a remarkable comeback for the politician of humble origins who rose to become Jamaica's first female prime minister in March 2006 and then lost power after 18 months.

This time she beat Andrew Holness, a 39-year-old technocrat, who had been PM for just two months. "After being tested and tempered I stand before you a stronger and better person prepared to be of service to my country and people," she said, pledging to heal political divisions, boost the country's economy and ease poverty.

Simpson Miller is genuinely popular and has an unrivalled ability to project empathy with the poor and downtrodden. Her PNP party – nicknamed the Portia National party by US diplomats because of her "messianic" sway over supporters – now has an unprecedented two-thirds majority in parliament.

This is enough for her to change the constitution and a win a vote to convert Jamaica into a republic. But she then has to put her plan to a popular referendum.

It is not a foregone conclusion that she will succeed, Laurence Allen, a Jamaican analyst with IHS Global Insight, said: "There is no clear view which way the Jamaican population would vote. It [a referendum] would be a bit of a gamble.

"There is broad sympathy for Jamaica being in full control of its constitutional arrangements and government. But balanced against this is wide and popular respect for the current Queen."

Additionally, Jamaica has more urgent problems to deal with: high unemployment, a massive debt to GDP ratio of 130%, and a substantial dependence on tourism from the crisis-hit US, Allen said. The island is also a victim of geography, stuck midway between drug-producing countries in the Andes and drug consumers in North America.

"There are so many challenges. It [reform] could well slip down the priority list fairly quickly," Allen predicted, adding that a referendum was unlikely before 2014/15, somewhere towards the end of the government's five-year term.

In her acceptance speech Simpson Miller said her government would "ease the burdens and pressures" of sinking living standards and rising poverty, and would pursue a tight fiscal policy while co-operating with the IMF and striving to "balance the books and people's lives". Urging reconciliation she said: "We will seek to make this country one of brothers and sisters, not of rivals and victims."

Her party's overwhelming parliamentary majority is part of a pan-Caribbean trend against incumbent governments. Over the past two years ruling parties have been thrown out of office in Trinidad, St Lucia and Haiti, and forced to share power in Guyana.

But it was also due to a scandal that enveloped Holness's predecessor, Bruce Golding, who stepped down as prime minister late last year. Golding was roundly criticised for dragging his feet over the extradition to the US of a powerful drugs baron, Christopher "Dudus" Coke.

Golding's administration opposed the US's request, before reluctantly sending police and military to arrest Coke in May 2010. Some 76 people died in ensuing violence, many apparently at the hands of government forces.

Leaked WikiLeaks cables reveal that US officials in 2007 correctly predicted Simpson Miller would bounce back from election defeat. They describe her speech to her party's conference, noting how she addressed colleagues as "comrades", a nod to the PNP's socialist roots.

"It was very clear that Portia still has a special place in the hearts and minds of the majority of the PNP faithful," one diplomat wrote, noting the "rhythmic music", "background singing" and songs praising Portia.

He added: "At times the convention swung between a Portia lovefest and a Christian revival session. Peter Tosh's reggae version of the 27th Psalm was frequently played, and also very well received by the party faithful."