Instead of doing a backup you can do an export of a single site and then import that to the other application. (if it's not possible to do an export because the original application doesn't exist, then you'll have to restore the web application temporarily and then do an export of the site)
Use the stsadm command line to do this (C:\Program Files\Common Files\Microsoft Shared\web server extensions\12\BIN\stsadm.exe -help export)
Export: stsadm -o export -url http://intranet/SiteDirectory/testsite/ -filename testsite.bak
Import stsadm -o import -url http://portal/SiteDirectory/testsite/ -filename testsite.bak
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