Android 1.5 Dialer App - Exploit Block
I just tested my own phone by loading Dylan Reeve's web page and to my surprise the Lookout app I have installed stopped it. I guess Lookout also functions as a dialer. According to this page there is a version that supports 1.5 (although I'm not sure if that version does include protection from USSD attacks).

I haven't tried it myself but, according to this post you can download apk files from the play store to your computer. If you succeed just copy the apk to your phone manually and install.