Rabbits are part of Annex I, Part B:
Species of pet animals
Dogs (Canis lupus familiaris)
Cats (Felis silvestris catus)
Ferrets (Mustela putorius furo)
Invertebrates (except bees and bumble bees covered by Article 8 of Directive 92/65/EEC and molluscs and crustaceans referred to respectively in points (e)(ii) and (e)(iii) of Article 3(1) of Directive 2006/88/EC).
Ornamental aquatic animals as defined in point (k) of Article 3 of Directive 2006/88/EC and excluded from the scope of that Directive by point (a) of Article 2(1) thereof.
Birds: specimens of avian species other than those referred to in Article 2 of Directive 2009/158/EC.
Mammals: rodents and rabbits other than those intended for food production and defined under ‘lagomorphs’ in Annex I to Regulation (EC) No 853/2004.
For them are these rules:
Pet animals of the species listed in Part B of Annex I
Conditions applicable to the non-commercial movement of pet animals of the species listed in Part B of Annex I
Insofar as the Commission has adopted a delegated act pursuant to Article 19(1) with regard to pet animals of one of the species listed in Part B of Annex I, the non-commercial movement of pet animals of that species into a Member State from another Member State shall be subject to compliance with the conditions laid down in paragraph 2 of this Article.
Pet animals of the species referred to in paragraph 1 may be moved into a Member State from another Member State only if they fulfil the following conditions:
(a) they are marked or described according to the requirements adopted pursuant to Article 17(2);
(b) they comply with any preventive health measures for diseases or infections other than rabies adopted pursuant to Article 19(1);
(c) they are accompanied by an identification document duly completed and issued in accordance with Article 29.