Yes, there is a University of Melbourne study!
- Breast-feeding and atopic disease: A cohort study from childhood to middle age,
Melanie Claire Matheson, Bircan Erbas, Aindralal Balasuriya, Mark Andrew Jenkins, Cathryn Leisa Wharton, Mimi Lai-Kuan Tang, Michael John Abramson, Eugene Haydn Walters, John Llewelyn Hopper, Shyamali Chandrika Dharmage, The Journal of allergy and clinical immunology 1 November 2007 (volume 120 issue 5 Pages 1051-1057 DOI: 10.1016/j.jaci.2007.06.030)
They based on the results of the Tasmanian Longitudinal Health Study (TAHS - sic.) which started with 8,500 children - although the abstract doesn't mention the sample sizes they used.
At age 7 years, exclusively breast-fed children with a maternal history of atopy had a marginally lesser risk of current asthma than those not exclusively breast-fed (odds ratio [OR], 0.8; 95% CI, 0.6-1.0). However, after age 7 years, the risk reversed, and exclusively breast-fed children had an increased risk of current asthma at 14 (OR, 1.46; 95% CI, 1.02-2.07), 32 (OR, 1.84; 95% CI, 1.06-3.3), and 44 (OR, 1.57; 95% CI, 1.15-2.14) years. Exclusively breast-fed children also had a reduced risk of food allergy at age 7 years but an increased risk of food allergy (OR, 1.26; 95% CI, 1.1-1.5) and allergic rhinitis (OR, 1.2; 95% CI, 1.0-1.3) at 44 years.
The ORs (Odds Ratios) aren't huge. You aren't condemning your child to certain asthma (or protecting them outright) based on your feeding choices. Other factors may be stronger.
Exclusively breast-fed babies with a maternal history of atopy were less likely to develop asthma before the age of 7 years, but more likely to develop asthma after the age of 7 years.
The current recommendation to breast-feed high-risk infants for protection against early wheezing illness can be confirmed. However, the recommendation should be reconsidered for protection against allergic asthma and atopy in the longer term.
The do mention that the existing literature is contradictory. Perhaps this surprising result of reducing the short-term risk but increasing the long-term risk explains some of the difficulty.