Praise be to Allah, the Lord of the Worlds. Mummification of an animal involves taking out its intestines and stuffing it with chemicals to prevent decay and preserve natural form. Mummified animals are of two types.
First, animals whose meat is lawful, such as camels, cows, sheep and some birds. Mostly, people don`t mummify this type because doing so is a waste of money and they tend to make use of every part of such animals. Second, animals whose meat is unlawful, such as dogs, lions, falcons, and the like.
According to our Madhab, Shafie, the general rule is that it is prohibited to kill animals except the harmful, because Islamic Law forbids killing animals for no need, save for food. By virtue of this, exemplary punishment is prohibited as well. Al-Bayhaqi have dedicated a whole chapter in his book, "Al-Sunnan al-Kubra", entitled "Prohibition of killing animates save for food."
He added the Hadith in which Abu Baker advised the soldiers leaving to Sham (Syria), " Do not slaughter sheep or camels except for food." Imam Tabarani related in "al-Mou`jam al-Awsat": "The Prophet (PBUH) forbade exemplary killing." Imam Ibn Hajar said, "He ordered that if we kill, we kill well and forbade exemplary killing."{Fateh al-Bari, 5/42}.
Undoubtedly, mummification is a flagrant violation of the concept of mercy, enjoined by sharia, towards animals. If the animals were mummified for scientific and educational purposes, while there is no alternative, then there is no harm in doing so, because conducting experiments and the useful scientific findings resulting from that is amongst the objectives of Sharia. As for linking the mummification of that rabbit with the sacred months, that is irrelevant.
In conclusion, mummification of animals for the sake of study and research, while there is no other alternative, is permitted, but as needed. However, if it was done for the purpose of adornment and boasting, then it isn`t permissible, because that is a waste of money. And Allah knows best.