As far as I can figure, she should be between sixteen and eighteen here. Absolutely no younger than fourteen, if this is a Y1 story, but since Joker's a regular in Arkham with a relationship with Bruce, and Bats has a measure of respect and liberty from Jim and the GCPD, we're looking at two or three years into his career; any further, four years, puts it right about when Babs became Batgirl, which as per *her* Y1 was around 18 or 19 for her (so, basically, yeah, we're still looking at that 8-10 year difference from pre-Crisis).
But hey, Kreisberg trying to rob a female character of her seniority and polish up her sex appeal by stripping multiple impossible years off her - what else is new?