After winning Australia's Next Top Model Alice appeared in an ad campaign for Green With Envy, a fashion boutique in Melbourne, and on the cover of Pages, an Australian fashion magazine. She modeled for several months in Singapore, appearing on the covers of Luxury, and Luxx Living magazines. During her prize vacation to New York, Burdeu was signed by Elite Model Management, who helped her secure jobs in the Fall/Winter 2008 New York Fashion Week shows of designers including Proenza Schouler, Marchesa, and Marc Jacobs.
Burdeu has appeared on the covers of Vogue Australia, Verse, and Luxury, as well as in fashion editorials for Women's Wear Daily, Velvet, Elle UK, Marie Claire Italy, and Numéro Korea. She has walked in runway shows for designers including Louis Vuitton, Alexander McQueen, Dolce & Gabbana, Marc Jacobs, Christian Lacroix, Jean-Charles de Castelbajac, Jil Sander, Lanvin, Lacoste, D&G, Shiatzy Chen, Sonia Rykiel, andAlex Perry. Burdeu has also appeared in campaigns for D&G, Sonia Rykiel, Napoleon Perdis, Mimco and Blumarine.
In February 2008, Burdeu was featured in Models.com's Top 10 Newcomers of Fall 2008, and was touted to be one of the rising stars of the high-fashion world by Style.com.
In the latter half of 2008, Burdeu took time off from the modeling world, skipping the Fall/Winter 2009 fashion weeks altogether.
In 2010, Burdeu re-appeared in the fashion world, after studying at the Royal Melbourne Institute of Technology, during New Zealand Fashion Week; She appeared in 19 shows during fashion week. She was featured in the October issue of Fashion Trend magazine and modelled for Fleur Wood's 2010 winter campaign In 2011, Burdeu resigned with Elite Model Management in New York and signed with Elite Model Management in Milan for the first time. Since this, Burdeu was featured in an editorial in Vogue Australia in February 2011, Tokion Factory in January 2011 and modelled for Country Road, Ellison, Juli Bala and Mindfood.
During Fashion Week Fall/Winter 2011, Burdeu walked for Chado Ralph Rucci, Honor, Naeem Khan and Timo Weiland at New York Fashion Week, Giles at London Fashion Week, Giorgio Armani, Emporio Armani, Piazza Sempione and closed for Philipp Plein at Milan Fashion Week. Manish Arora and Damir Doma at Paris Fashion Week.