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It depends on how her credit history looks - AAOA, utilization, income, inquiries. Assuming this stuff checks out her being an AU shouldn't reset her clock before she can get her own card.
Looks great. As long as no baddies (score >720ish), she should have no problem with an approval. My sister did the same thing with Amex and Discover last year. She was added as an AU and then applied for her own cards a month later. Not Barclays but I don't see why they wouldn't be similar.