You can't set up clustering or mirroring, but you can set up a poor man's "log shipping." Whatever you're using to generate the backups of your database (Task Scheduler or some other scheduling system) could be used to copy the backup to another install of SQL Server Express and then use SQLCMD to apply the backup.
Also, keep in mind that in a clustering situation, there is still but one copy of the database. Microsoft clustering with SQL Server is a shared nothing configuration. That means the disk belongs to only one physical server at a time and the databases reside on that physical server. The reason that's important is to think about why the DB crashed. If it crashed due to corruption or the physical disk failure, you'd still be down in a clustering situation. Now, if the physical server crashed, then in a clustering situation you'd failover, meaning you'd have a 30 second to a few minute downtime.