In the long names of countries, if the name of the country is used at all, the article is usually dropped.

La Belgique: le Royaume de Belgique
Le Luxembourg: le Grand-duché de Luxembourg
L’Allemagne: la République Fédérale d’Allemagne, in which “d’” abbreviates “de”.

Similarly “l’Australie” is “le Commonwealth d’Australie”; “l’Andorre” is “la Principauté d’Andorre”.

“La République de l’Inde” is a weird exception I just discovered and to which I have no rational explanation.

Moreover, “d’” is the elision of “de” only (either the preposition or the article). “Du” is never elided, as it contracts “de le” only. “De l’” is not contracted, regardless of the gender of the following name.

La boutique de la boulangère
La boutique du boulanger (“du” contracts “de le”)
La boutique de l’épicière (feminine)
La boutique de l’épicier (masculine, but the elision prevents the contraction)