It should be noted that none of the suggested alternatives are as precise and natural as your original! Which explains native English speakers’ use of the verb ‘to get’ despite having some detractors. I haven’t done it yet. (Is similar but, like the other suggestions, has a slightly different nuance)

That's a good question. Every student of English should ask themselves this question every time they feel tempted to use the word "get". People like to use that word because it avoids the necessity of thinking. Indeed, you could probably speak English using only "get" and no other verb. I intend to do it, but haven't yet. I haven't found time for it yet. I haven't found time to do it yet. I haven't been able to find time for it yet. I haven't made time for it yet. or you could add an excuse: I've been too busy to do it. I intend to do it but other duties keep calling me.

I haven't gotten to it yet I haven't attended to it yet I am yet to do it

I haven't had time to do it.