Child bike seat usage when approaching max weight
Even if you decide to buy the seat now, presumably there'd be an issue as she grows? And by the sounds of things, it won't be long before she passes the upper limit. 

So I'd look at other options, which as I see it, are:

a trailer



one of those things where they're sitting on their own saddle, over their own wheel, but are actually being towed by you



or last, get her her own bike. From experience, this one has pros and cons. The obvious pro is to get them cycling as soon as possible, the con is that until they become pretty proficient, they ride mightily slowly!

While I was googling, I also came across this article which might help (and this is where the pics came from).