Shade an area under density curve, to mark the Highest Density Interval (HDI)

I thought this should be straightforward, but I'm lost, despite tons of information online.

My Problem: I have a vector of data points, for which I want to plot a density curve, then color the area under the curve to signify the Highest Density Interval (HDI). Naturally, I'm trying to achieve this with ggplot2 package, and specifically with qplot(), since my data comes as a vector, and not a data frame.

Reproducible Example

library(ggplot2)
library(HDInterval)

## create data vector
set.seed(789)
dat <- rnorm(1000)

## plot density curve with qplot and mark 95% hdi
qplot(dat, geom = "density")+ 
  geom_vline(aes(xintercept = c(hdi(dat))))

So I get this:

But what I really want is something like this:

Is there a simple way to achieve this with ggplot2::qplot?