However POstgis 2.1 is compatible with you current postgres option.
So as suggested you can upgrade postgis (see hard/soft upgrade), the upgrade postgres.
By the way postgis is very easy to compil with ubuntu (use package system to get dependecies, then simply sudo ./autogen.sh, sudo ./configure, make , sudo make install)
I would use normal pg_dump and pg_restore for the DBs and not utils/postgis_restore.pl. Also, AFTER I backup all databases and everything else, you could try to upgrade Postgis without upgrading PostgreSQL by buliding from source e.g. http://trac.osgeo.org/postgis/wiki/UsersWikiPostGIS21Ubuntu1304src. There it says that Postgis 2.1 could be used with PostgreSQL 9.1. This will give you access to Postgis 2.1 features without reinstalling everything.
Of course normally I would not upgrade if this is an 1-2 years project, unless I 100% need Postgis 2.1 features not present in 1.5.