Given how Joker beat Harley, sometimes just for fun, it's no wonder she'd have trouble giving birth.
There are other options (IVF?) and given the technology and magic the League has access to, they might have been able to fix it, then again Joker was a thorough bastard.

I can see Harley being a high maintenance woman with self esteem given how she's been treated, good that Vic is such a omantic.
Bruce Wayne giving Harley away was funny, and I bet the tried to get out of it until Alfred gave him that 'look' of disappointment until he made the correct decision.

Wonder if Harley trying for a baby was a wake up call for other women in the League, that biological clock is a ticking girls.

So the little girls new Name will be Heather Sage, I'm sure Poison Ivy would love that name.