Using Google and other online dictionaries I came up with 'Terrae Futurum'. Is this the best way to present the idea of how the Earth could look in the distant (billion years) future?
First of all, Google Translate is horrible with Latin and is not to be trusted. It has relevant components to it, but the details go awry. If you want a reliable online Latin dictionary, check this list of ours.
The word terra is more like "land", "country", or something of that kind. For the whole planet the more suitable word is tellus1. This is a feminine word, so the adjective2 futurus should go into the singular feminine form futura.
It is possible to use terra as well, but I find tellus more appropriate. There seem to be regional differences in preference, but both are valid options. They both take the same form of the adjective.
The future Earth is thus tellus futura or terra futura.
1 The plural is tellures instead of telli if you need it; don't be fooled by its ending in -us.
2 It's really a participle, but it can be treated as an adjective for many practical purposes.