Quantum spin liquids (QSLs) are intriguing states of matter in which quantum fluctuations are sufficiently strong to destroy any long-range magnetic order. To date, one of the best experimental realisations of such a system is herbertsmithite, ZnCu3(OH)6Cl2, but the exact nature of its QSL state remains a matter of debate. Here, we propose to explore Zn-doped barlowite, ZnxCu4-x(OH)6FBr, by muon spin relaxation (muSR). Like herbertsmithite, barlowite contains kagome layers of Cu2+. The x = 0 member of the series undergoes a magnetic ordering transition ~15 K, but the effects of doping the system with non-magnetic Zn2+ ions are yet to be fully explored. muSR has played a crucial role in developing our understanding of herbertsmithite over the past decade. Here, it will provide an important means to determine whether or not Zn-doped barlowite realises a new paradigm in the search for QSLs.