When Kabuto asked Tobi for alliance he showed five Akatsuki members' corpses, and one of them is Nagato's. But then Tobi encountered Konan to get information about Nagato's Rinnegan. Why was Tobi looking for Nagato's body when he already has it? Or is there something I'm missing?
The Summoning: Impure World Reincarnation needs only some of the DNA as it says in the wiki:
Before this technique can be performed, the user must first acquire some of the DNA of the person they intend to reincarnate. Kabuto remarks that this basically amounts to grave-robbing, although blood stains or organs salvaged after the target's death also work.
A little summary, about what happened and why Tobi wanted to find Nagato's real body.
Tobi feels personally betrayed when he learns that Nagato gave his life to revive the villagers of Konoha, believing the Samsara of Heavenly Life Technique should have been reserved exclusively for his Eye of the Moon Plan. He is also confused, believing Nagato to have been very firm in his convictions and thus not likely to give up so willingly. He tracks down Naruto not long after Nagato's death and asks him what he could have said to sway Nagato, but is unmoved by Naruto's claim that Nagato truly did desire peace. With Nagato gone, Tobi is forced to seek out his corpse and take his Rinnegan to fulfil his ultimate plans. When he finds Nagato smiling at him, he interprets it as Nagato continuing to mock him even in death.