My understanding is that it is something that the Telstra Mobile network is capable of doing, however I have only ever heard of it on business mobile broadband services, never on an actual mobile service though.
I would expect it would be something you would need to discuss with Boost Support to see if they are able to add it to the service, personally I would be a little surprised but it is possible.
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Using static IP addresses on home networks provides slightly better protection against network security problems than does DHCP address assignment.