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Working (either paid or unpaid) is prohibited under the terms of a visitor's visa I'm afraid, they are very strict about that and it may affect any future visa application she makes if she breaches the visa by working.
Spouses who obtain a spouse visa are permitted to work under the terms of that visa but it is a a pre-requisite that she intends to settle here permanently I'm afraid.
If she were eligible to apply for a Tier 1 Highly Skilled workers visa under one of those categories then she could make an application in that way but the application must be very throughly prepared and from the point of submission it generally takes about 8 weeks for them to reach a decision (& usually longer).
In view of the short length of time before she intends to depart I'm afraid he only option is a visitor's visa (without working)
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