I just tested my own phone by loading Dylan Reeve's web page and to my surprise the [Lookout](https://play.google.com/store/apps/details?id=com.lookout) app I have installed stopped it. I guess Lookout also functions as a dialer. According to [this page](https://support.lookout.com/entries/21906203-android-1-5-and-1-6-device-support) 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](https://android.stackexchange.com/a/28139/7574) 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](https://android.stackexchange.com/q/5566/7574).