Postgresql – do a backup without extension functions

But that is 9.1. - Is pgadmin connected to the wrong postgresql?

Yes.

It appears that you're connected to your 9.1 server, suggesting that 9.1 is still running.

Do pg_lsclusters to see what PostgreSQL installs you have and their status.

Each runs on a different port. If you want to connect to 9.3 you need to check what port it runs on and connect PgAdmin to that port.

As @a_horse_with_no_name wrote pg_dump and pg_restore cope with PostGIS things without problems. At least since PostGIS 2.0, previously (before PostGIS became an extension) you might had to change paths of the c-library used for geometry-functions.

In PostgreSQL since 9.x ist is also fairly easy:

1. backup at the original databse with pg_dump
2. at the new system:
   1. create a new database
   2. login to that new database and run CREATE EXTENSION postgis;
   3. restore the backuped file with pg_restore to the new database

That works for me as well on windows as on linux, you could even use PgAdmin for it.

Note: the version of pg_dump of the original (backed up) system may not be newer than of the new system - see https://stackoverflow.com/q/12836312/8957103