The installer.php is independent of WordPress, in other words it doesn't rely on any of the core wordpress files. So updating to 3.7 shouldn't cause this issue as I have updated a dozen or so sites to 3.7 without any issues. The issue might however reside on your host or web server and how they treat large minimized packages. The developer version has a similar fix for this issue that might address the issue your describing.
If you can give the latest version a try it may have your fixes for the issue your seeing. The very latest version can be found by following these instructions:
-> Browse to http://wordpress.org/extend/plugins/duplicator/developers/
-> Look for the section "Other Versions"
-> Click on "Development Version" and download the zip plugin file
-> Uninstall your current version and install this one
-> Note: The version number may still be the same as the public line but the source code is different.