Dowding graduated from the University of Western Australia with a Bachelor of Laws, and he subsequently worked as a solicitor and barrister.

He entered the Burke ministry when Labor won the 1983 state election and changed portfolios several times over the ensuing years due to cabinet reshuffles.

At the 1986 state election, Dowding transferred to the Legislative Assembly, the parliament's lower house, winning the safe seat of Maylands.

Burke picked Dowding as his preferred replacement, with a secret opinion poll showing that he was the best candidate for the party to choose.

[2] His parents were Keith McCallum Dowding, a high-profile Presbyterian minister and left-wing political activist, and Marjorie Stuart D'Arcey, who died of suicide when Peter was eight.

Keith Dowding was also a member of the Labor Party and had attempted to enter Federal Parliament several times,[7] but he was expelled in the early 1960s for his opposition to the White Australia policy.

[8][6][9] Dowding earned a Bachelor of Laws degree from the University of Western Australia in 1964, and was admitted to the bar in December 1966.

[8] The case gained notoriety when Dowding proved that the police officers involved in the incident had swapped their name badges to prevent them from being identified.

From March 1975 until April 1976, Dowding was on the Kalamunda Shire Council, and in 1976 and 1977, he worked as a notary public with the Aboriginal Legal Service in Port Hedland, during which he met his second wife, a Ngarluma woman from Roebourne.

[11][10] In 1977, Dowding represented defeated Labor Party candidate Ernie Bridge in a landmark case in the Court of Disputed Returns.

At the 1977 state election, Bridge was defeated by Liberal candidate Alan Ridge by 93 votes in the electoral district of Kimberley.

The Liberal Party had worked to disenfranchise Aboriginal voters, many of whom were illiterate, by having lawyers stand outside polling stations to question their right to vote.

Dowding was well supported by the province's large Aboriginal population, having promised to help them gain land rights and self-management.

[26] In his role as minister for employment and training, he embarked on a tour of Europe, where he developed an interest in Sweden's regulated economy.

[29][31] Other contenders were David Parker, Bob Pearce, and Julian Grill,[30] however they all pulled out of contention before the 30 December Labor caucus vote due to Burke's influence, the opinion poll, and the desire for the party to be united.

[37] In November, the Labor Party paid for a two-minute prime time television commercial where Dowding made a speech promising that no more taxpayer money would be spent on Rothwells.

The budget also included the release of two thousand state housing homes for sale, and the promise to build an electric railway line to Joondalup at a cost of $124 million.

His defence lawyers had argued that Dowding and acting energy minister Grill had ordered Lloyd to pay off a Rothwells debt using a $15 million cheque.

In January 1990, Lloyd was found guilty of acting improperly, making him the first person convicted for an offence relating to WA Inc.[41][42][c] After that, opinion polls showed support was as low as 32 percent.

[43][41][45] In early 1990, Dowding travelled to the World Economic Forum in Switzerland, after Parker assured him that nothing would happen to his leadership while he was gone.

[46] State Secretary Stephen Smith, FMWU Secretary Jim McGinty, and seven Labor politicians – Lawrence, Parker, Taylor, Kay Hallahan, Keith Wilson, Geoff Gallop and Pam Beggs – met together to discuss Peter Dowding's leadership, all deciding that he should be forced out.

[47][43] He returned early from the World Economic Forum on 8 February in order to shore up his leadership, spending the next several days speaking to party members in an attempt to ensure their support.

[43][50] On that day, Lawrence promised to end WA Inc.[51] Dowding criticised the leadership challenge, saying that the timing was premature and was done to help Labor win the federal election, rather than for what's good for the state.

[55][56] Dowding testified in front of the commission in November 1991 regarding his dealings with Laurie Connell and Alan Bond, the bailout of Rothwells and the purchase of the Kwinana Petrochemical Plant.

"[59] Dowding responded by saying that some of the commission's judgements of him were wrong, but that he was relieved the report did not find any of his decisions were corrupt or for financial gain.

[63] In August 2023, he released a book co-authored with Ken Spillman about the life of his uncle, Bruce Dowding, who was part of the French Resistance and worked to smuggle Allied servicemen out of Nazi-occupied France in 1940 and 1941.