Economy, business, first?

Does she have status or loyalties on any airline/alliance?

Reason being, while OW offers the most flexibility and mileage-earning opportunities, if her itinerary is relatively simple, a 29,000 mile Star Alliance RTW might be somewhat cheaper.

She'd probably have to originate in someplace like Copenhagen or Stockholm if the pricing posted in WearyBizTravlr's spreadsheet (see price sticky above) is still current when she starts, but for example CPH-LHR-YYZ-CLT-BZE-CLT-LAX-SYD-SIN-CPH is only 27,000 mi and change. She could find an inexpensive ticket to get to CPH and back at the start/end.

Otherwise starting in France (for both Oneworld and Star) is relatively expensive compared to other origin points relatively nearby.

The exception to this is if she's riding in economy, in which case originating in Britain is probably the cheapest alternative (but NOT for business/first.)

But the itinerary is certainly doable using either alliance.