There are a couple of options to backup a layer in Quickmap. The best way to backup a layer is to right click the layer you want to backup, then click Layer Properties, you can then find out the database name and manually take a copy of that database (how you take a copy of the database depends on the type of database – the default Quickmap mdb files can just be copied, but if you have connected Quickmap to another datasource such as MS SQL or Oracle, then you’d need to follow the appropriate steps to backup that database – speak to your IT staff for advice here).

You might be tempted to Export a layer to back it up, but it’s worth noting that exporting a layer transforms it into the format that you export it to, and may change the way the data is stored. It’s not a recommended backup method because it’s not an exact copy of the data.