Well, maybe I'm a little cynical but I don't see the OP taking her DD in to see the physician as the magic bullet that a lot of people think. If her child is 45 pounds at 19 months, 99 out of 100 physicians will look at their chart and then tell the OP to put her on a diet. Period.
We're on the other side of it. My DD is almost 5 and she's about 32-34 pounds. That's around the 3rd-5th percentile. Every doctor who ever looks at her tells us to feed her ice cream, as much as she'll eat. Uh, yeah, converting her diet to sugar is a good way to feed a growing body. Apparently every calorie is equal, a calorie of ice cream will build her muscles and eyesight and organ functions and brain and immune system exactly the same as a calorie of steak or brown rice or whatever. And raising her on ice cream will lead to excellent dietary habits and health down the road. Sorry, I don't buy it, and I don't put a huge amount of trust in the average pediatrician's nutritional advice.
Now, am I saying that there's nothing amiss with the OP's daughter? No, I have no idea. Sounds like she could have a problem, sounds like she could be fine. OP, I'd encourage you to do the legwork yourself. Look at the WHO charts, especially weight for height (NOT weight for age): http://www.who.int/childgrowth/standards/en/
Are you familiar with symptoms of juvenile diabetes? I am not, but if I were you I'd have a look. Google conditions that might be related to unusual size in small children.
If anything rings a bell, go to the doctor and express the specific concern. "Could she have diabetes? Can we get a test?" (Or whatever).
But honestly, if you've done her legwork and she seems perfectly healthy than I would just keep on keeping on. Her diet sounds excellent (I'm frankly jealous, as the mother of a non-eater), her energy sounds excellent, and she has a family history of similar growth curves (we do too - both me and DH grew the same way that DD is growing, so we're taking a chill pill on it).
Oh, and I don't put much store by anecdotes but here's one for you anyway. My mother's best friend's daughter was 40 pounds by 18 months. Today she is 24 years old and the most gorgeous, athletic person I have ever seen in real life. Her being gorgeous is irrelevant but my point is that far from being obese or unhealthy, she is strong and active - so much that she has attracted the attention of some TV producers. She, too, was never "fat" looking, just a really "big" baby.