pg_dump in 1G VPS crashes

I'm trying to run pg_dump on a relatively small database (2G), but pg_dump keeps crashing with an out of memory error.

du -h --max-depth=0 9.4 1.9G 9.4

The command: pg_dump -Fp -h "$HOSTNAME" -U "$USERNAME" "$DATABASE" | gzip > $FINAL_BACKUP_DIR"$DATABASE".sql.gz.in_progress;

Any ideas on how to allow the dump to happen?

Thanks