I know there are other moms of skinny babies on here, and I just wanted to share some success! My DD has been dropping weight percentiles for months, and by 15 months she was down to the 5th percentile (50th for height). My pedi recommended lots of cream cheese/butter/olive oil on foods, making her oatmeal with cream or half-and-half, etc.
We went in for a check-up today (she's been really off and refusing to nurse the last few days -- turns out she's getting some top and bottom molars at the same time) and in 15 days, she gained 1 lb., 12 oz. She was at 19 lbs. 4 oz at her 15-month appointment and is now 21 pounds!
I was really, really encouraged at seeing results so quickly. There's definitely some extra effort involved in adding healthy fats to her meals and putting PB or cream cheese on the snacks I used to give to her plain (rice chex, graham crackers, banana bits) but it's working. I'm so relieved!

Re: High fat diet is working! She gained weight!
Yay!
I will have to try some of those ideas. We were told no PB until 2 though.
My dd was also 17 lbs at her 12 month appt, and her height was in the 42nd %tile--so she was almost exactly your daughter's size. No concerns here, either, really. She's petite. It's fine! Kids come in all sizes, and my DD's smaller size has had no negative effect on her developmental growth whatsoever.
If she weren't consistently gaining, or if her weight were so low that it affected her overall health in any way, then I'd look into weight-gaining techniques. However, since that isn't the case for my baby, I don't see the need to do a particular diet to get her to gain more weight, and my pedi supports that. I figure she'll eat what she needs and be fine. :-)
(To OP, I am glad that you are having success!)