Bella finds out from J's "assistant" on the stoop that he deals in papers. This is why Alice sent Bella to J's office in a bad neighborhood, instead of his nicer office: she wanted Bella to find out what J does. Alice was giving Bella a way to make sure that Renesmee lived on. Since Alice's visions change every time someone changes their mind or makes a new decision, she couldn't be sure how the confrontation with the Volturi would turn out. So she wanted to give Bella a chance to get everything in order for Renesmee, in case an escape had to be made. Jasper has used J in the past to make papers, undoubtedly because the Cullens need to continue to make themselves younger and to give themselves new identities. So Alice knew that J would be able to help Bella make a new identity for Renesmee in order for her to escape the Volturi and have a chance to keep on living, even if the rest of them died.