Profile a db connection time?

Sorry if this is silly , but I have series of network outages and wanted to
understand if I can profile a psql connection to various parts of it
initialling a connection
Like when using hostname, resolving dns
the time to actually establish a db connection and then the time to parse
the query and run the query and time to return the results
I know a lot of the answers could be
Why not do a dns check before the connection,
run vacuum analyse to check only db time and do not return any row, and
then run with returning the rows and do a diff etc.
Am I asking something that makes sense?
Like google chrome does for page loading etc ?

--

Regards,
Vijay