Use this tool to export your data as XML from Doit.im because they refuse to build an exporter for the data that you own!
These instructions are written for Chrome, but they probably work just as well in other browsers (just different keyboard shortcuts).
Log in to Doit.im using your browser.
Click on the "Search" icon on the top right and click on "advanced":
Now without setting any filter parameters, click "Save as a Filter":
Now give your new filter a name (e.g. "All Tasks").
At the left bar, under Filters, you will find the filter you've just created. Open this filter. You might need to be patient because the list might be big.
Press ctrl + shift + j (command + option + j for Mac) to get to the Developer/Javascript console. Paste the contents of the doitExport_XML.js file into the javascript console. If all works well, your browser will have now downloaded an XML file with all your data.
If you want to repeat the export, you can re-use a previously created filter.
I had plans to change the output so that it can be imported by proper services like Todoist but I have chosen to do this manually so there is not going to be a converter/importer from me. Feel free to build one!