The injunction to name the animals is not a common subject, but it is depicted in Creation series. An example close to Brueghel is the cycle of paintings by a fellow Netherlander in Italy, Jan Soens. His series divides the events of creation somewhat oddly: Adam appears (apparently somewhat stunned) in the picture usually called God Dividing Light from Dark, while the next scene seems to conflate the quickening of Adam with the injunction to name the animals. Soens’s paintings, now in Parma, are based on a series of prints by Johannes Sadeler after Marten de Vos. See Meijer, Parma e Bruxelles, 56-66.
I could not see the signature or date in the very clear photograph at the RKD. Animals in this version, at least the lions, are closely related to those in the Paris "Allegory of Earth" which I think must date from ca.1605 or so. The horse in the present painting, though, is much more primitive, almost naive. In contrast to his later versions of this theme, where animals are insistently paired, here pairing is uneven. Lots of creatures appear that don't "belong" together -- so again, not those semi-taxonomies of later works.
Re: dating, query if this could be Paradise painting from Giustiniani collection? It was a work on copper listed in 1601 inventory as "same size" as a bunch of other Brueghels he owned, ie., the standard Jan size as this one is. This is the only surviving Paradise that meets those criteria (approximate date, size, support).
Note also that another painting in the Doria Pamphili of God Creating the Animals (inv. 452, panel, 72 x 140) reuses some of the same animals from this painting. Berger, in her book on Bril, accepts that work as being by Bril but suggests that the animals might be by Brueghel. She dates it to before 1600; given its large size it would have to have been done in Rome and I don't believe that they were by Jan back then. The animals lack the liveliness and refinement of his, although of course they are much larger. There are several other related pictures in the Doria Pamphilij which Berger does not accept as Brils (#s 473 & 5381). The interconnections between all these works need unravelling.