Her stage work in Australia includes the title roles in Shirley Valentine and Educating Rita, and as Maria Callas in Master Class, for which she won the 2002 Helpmann Award for Best Actress in a Play.

On stage, her performances with State theatre companies include Privates on Parade, The Matchmaker, The Seagull, Shirley Valentine (MTC), Master Class, Nicholas Nickleby, The Rise and Fall of Little Voice, Soulmates (STC), Duet for One, The Winter's Tale, Gigi, We Were Dancing (QTC), Twelfth Night, Blithe Spirit (SATC), Educating Rita, Medea and Shirley Valentine (Hole in the Wall, Perth).

Muggleton's commercial credits include HMS Pinafore (Essgee), Hello Dolly (The Production Company), The Book Club, Master Class (ICA), Annie (GFO/SEL/Macks), the original Steaming (Morley, Davis), Eureka!

[citation needed] Muggleton and Olsen also devised and co-produced Marvellous Party!, a production that celebrates the words and music of Noël Coward, and which had two sell-out shows at the Concert Hall in the Victorian Arts Centre, a highly successful Victorian tour and has been seen at Capers, Melbourne (2003 and 2004), Friends Restaurant (Hyatt) Perth, Edwards Waterfront Mandurah WA (2004) and Canberra's Teatro Vivaldi (2004).

came Darling It's Noel, produced by International Concert Attractions and directed by Rodney Fisher at the Sydney Opera House in May 2004 and at His Majesty's Theatre, Perth in June 2004.

In 2009, Muggleton and her business partner Bernadette Eichner founded Scene & Heard, a new acting school based in Sydney's Lane Cove.

In 2011, Muggleton started playing multiple roles in Love Loss & What I Wore at the Sydney Opera House alongside Magda Szubanski and Natalie Bassingthwaighte.

In March 2012, Muggleton went to Queensland for a role in Fatal Honeymoon, a feature film based on the death of Alabama woman Tina Watson on her Great Barrier Reef diving trip in 2003, shot for the American cable channel Lifetime.

Following this, she took to the road for a six-month tour of The Book Club which visited Brisbane, Sydney, Melbourne, Adelaide, Perth and many regional areas.

Midway through the tour she took a break to reprise her role in Blood Brothers at Brisbane's Cremorne Theatre, QPAC for two weeks in August.