katniss’s first memory of Peeta happens with baby clothes:
She tries to sell the last things she can to survive. When no one buys, she drops Prim’s old clothing in a muddle puddle and leaves them there. She’s too weak to survive, too weak to kneel down and pick them up. She gave up. She was going to let the community home take them— give in to the one thing she had fought so hard to prevent:
Then, Peeta tosses her the bread. She doesn’t tell us if she goes back for the threadbare clothing, she instead runs home to Prim.
He didn’t just save her life, he saved Katniss’s reason to live: preventing Prim from getting taken to the community home.
If we examine this more generally as a metaphor:
Katniss had given up on kids. She dropped the last hope she had about having children in that mud puddle. She spent all day in front of adults, none of whom spared her any food or help. She realized she could not care for herself, never mind a child. The only person who helped her reclaim her position as protector was Peeta.
She was forced to leave the dream of caring for the child behind until Peeta arrived. Until the bread.
So it makes sense he would ask for a child and ensure the safety to care for them in the epilogue. It’s her going back for the baby clothes. Only now, she’s not too weak to pick them back up.