As you say, this seems quite doable - the JDBC metadata retrieval
functions should be able to return most of what you need, though you may
need to rethink the GUI. It may be enough of a problem to draw a
readable ER diagram (where E=table, R=fk) showing just the table names
from a decent sized schema and disentangling it so not to many
relationship lines cross could be quite difficult. You may want to show
table properties (columns, keys, indices, etc) only by clicking on a
table and the same for a relationship.

Are you familiar with the Embarcadero (http://www.embarcadero.com)
tools? If not you could do a lot worse that download an evaluation copy
or two. Some of their stuff may be what you need and failing that you'll
surely get some ideas by playing with it.

If you may find that automatically producing a schema diagram that isn't
a tangled mess is sufficiently difficult that the way to go is to let
the user drag objects around to make the diagram readable and then save
the result. On start-up it should be easy enough to compare the saved
model with the actual schema. If they are the same there's no problem:
just show the hand-modified version. If they differ you'll need to do
something about it: either replace the diagram entirely or just patch it
to match the schema, again letting the user change any tangled bits.

HTH

I believe I have seen Eclipse plugin doing just this - probably
azzurri.clay. I played with it some time ago - you setup parameters like
database connection, user, password, database used - and it produces
picture or some structure with database schema.