Lydia and the Colonel by Catherine Bilson

Lydia Bennet came to Brighton for fun, flirting, and a husband in a red coat. She did not come to be watched over by Colonel Fitzwilliam, Darcy’s cousin, who is somehow both boringly sensible and far too handsome to be ignored.
When Wickham’s scheming nearly destroys her reputation in a single night, it is Fitzwilliam who intervenes, and Fitzwilliam who finds himself honour-bound to offer her the protection of his name. But the consequences of one reckless evening reach further than Brighton. Lydia’s choices threaten to cast a shadow over her sister Elizabeth’s chances at happiness with Darcy, and only a hasty marriage to a man she barely knows stands between the Bennet family and ruin.
It is not the marriage either of them imagined. He is a soldier with orders to sail for Canada. She is sixteen years old and has a great deal of growing up still to do. Three years and an ocean apart is a long time to wonder whether a hasty bargain can become something real.

A Pride and Prejudice variation for anyone who ever thought Lydia Bennet deserved better than Wickham.