Sounds a bit like baby led weaning (google it for a tonne of sites & info) to me, except for the starting at 4 months part, basically blw (I am getting organised early for when DD starts wanting some munchies!!) is recognising when bubs starts to get interested in actually eating food, as well as whether or not they are able to hold food (pincer grip) to eat it & sit up enough to eat it. The theory is that if they tick all those boxes then they are ready to start tasting things (because according to the ABA it is all about tasting & textures until a fair bit later) on their own. Oohparently, they are less likely to choke on a steamed piece of brocolli they can control eating on their own, than pureed brocolli one is shoving down their throats with a spoon....

As for your DD not yet 'getting it' I have heard of bubs just on this site alone that don't really start to want to eat on their own anywhere from 6 to 12 months, I'm sure those Mums with that experience will be able to set your mind at ease there.