Although your proposed translation, as amended in the previous answer, is grammatical (though certainly eyebrow-raising!), I would like to approach your question from an angle that might be more appropriate: How did Thomas Aquinas express this thought?
Fr. David Burrell's translation uses one verb ("to be") to express two ideas, and succeeds I believe. Aquinas divides these concepts expressed by esse, using the famous distinction between being (esse) and essence (essentia, also natura as used in your question, or even quidditas). This distinction forms the subject of one of my favorite opuscula of Thomas Aquinas: De Ente et Essentia.
I recommend reading the whole work through. The part that comes closest to expressing the idea of "To be God is to be 'to be'" is at the beginning of VI:
Invenitur enim triplex modus habendi essentiam in substantiis. Aliquid enim est, sicut deus, cuius essentia est ipsummet suum esse; et ideo inveniuntur aliqui philosophi dicentes quod deus non habet quiditatem vel essentiam, quia essentia sua non est aliud quam esse eius.
(Be careful with this last bolded statement, though, since he includes the caveat shortly afterwards: "Nec oportet, si dicimus quod deus est esse tantum, ut in illorum errorem incidamus, qui deum dixerunt esse illud esse universale." This is a crucial step away from pantheism.)
To fit the first phrase into roughly the same shape, I would thus translate: Dei essentia est ipsummet suum esse. You could take out ipsummet, but for me it adds the strange "what's going on here..." flavor that the repeated "to be" has in the English.