the "convex hull" would look like this:
___ _ _ _
|_ _| / \
____ ___ / \
___| | | |____ / \
|__ ___ | |_______| => |_ ________ |
just the outer points are connected in a way that all points are inside the new
polygon; an interesting geometrical problem, there are some algorithms available.
Possibly you could achieve a result similar to your drawing by upsizing all shapes
to an intermediate layer by an amount that's sufficient to close all gaps, the shapes will merge,
then downsizing by the same amount, the outlines should look like your drawing but
the gaps will stay closed.
Size resp. leHiSize() will not merge the shapes,
dbLayerSize() or "Tools - Layer generation ... GROW" should do the job.