The old Google Docs app would probably do the job, but it's been pulled from the App Store. The only way of getting it would be if you'd owned it before, in which case it might still show up under the Purchased tab of the App Store.
{I'm assuming that offline editing is a requirement, or you could probably get by accessing the mobile site in Safari}
Barring any other, so far undiscovered apps, I see two options. Upgrade your hardware, or use a different editor/format for your documents. You can still use Google Drive itself to sync documents. Many text editing and word processing apps support it.
In the case of hardware, even an iPad 2 would give you access to a newer iOS and the Google Drive app. There should be some fairly cheap ones available on
eBay, Craigslist, and other sites. I don't really recommend this as I suspect it is only delaying your problem by a year, at most. I newer model is indicated if you can afford it.
Depending on how much you need to stay in the Google Doc format and the Google ecosystem, you might even want to consider going with an Android tablet, or a Chromebook.
There are a great many text editor available that will sync to Google Drive, both for the iPad and other platforms. You can even use the version control and sharing features; though obviously not the built in editor and revision features. I have blogger friends who swear that you should only use text apps use plain text, markup language, and maybe some RTF for document creation and revision. They only take their stuff to an actually word processor when it comes time to print, or perhaps create a PDF. Neither of which is a common task for online writing.
Unless you need the features in the Google Doc editor, this may be a good choice. It eliminates almost all compatibility problems. It's a rare app that won't accept plain text and/or markup. The selection is slightly lower with RTF, but still better than depending on a word processor.
Without knowing more about what you are writing and for what purpose I can't make any suggestions (good or not) about the best approach. I recommend you throw out everything you know about what you think you need to do the task and start over with what needs to be accomplished. It may mean you just need to shift your workflow and apps around a bit, it may mean you need a completely new set of apps and services, or you might need to get new hardware; even if it means it's not Apple hardware.
Good luck.
