Can you please confirm your immigration status please?
Does the father of the child object to her settling in Britain?
I am afraid I'm going to have to go offline for a bit now, so I'll answer assuming that you are either a UK citizen or otherwise have indefinite leave to remain in the UK AND that the father consents to the child settling in Britain. If this is incorrect please specify and I will tell you if it is necessary to revise my answer.
In my view you are right to doubt. There is no advantage whatsoever that I can see from making an application separately for the child after the wife has already applied for her visa and, in fact, the UKBA will likely want to know why she has not applied for the child at the same time and what is to happen to the child in the interim before she makes her application.
If the child was to make a separate application after the mother's then there would also be a full application fee payable for the child, whereas if the child applied at the same time as the mother then there is simply an "add-on" fee to pay which is considerably less than the full fee.
Obviously a separate application would also significantly lengthen the amount of time it would take until both mother and child have their visas.
Certainly, separate applications do not appreciably affect the likelihood of either obtaining a visa - they will either get one or they won't based on the eligibility criteria and the cogency/credibility of the applications they submit, it will not depend on whether they supply separate applications.
A sundry point is that the organisational skills of the UKBA can, on occasion, be less than one would hope and two separate applications gives them two separate opportunities to get themselves in a pickle.
I suppose the only advantage one might argue is that if the mother has been granted the visa then a person could be more confident that the child's application would be accepted but I certainly think that the above outweighs this.
If the father objects to the child settling then this could cause problems both in terms of him contacting the UKBA in respect of the application and enforcing his rights as a father under Chinese law, upon which I am not an expert I'm afraid.
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