Fishing rods are available at Rank 14, and cost about $32. You can purchase them from your brochure. Just hold [D-Pad: Left] to open the brochure and order it. It will instantly appear in your inventory.
Killers and griefers are around every corner in Red Dead Online. That makes fishing one of the most dangerous activities you can try. If you stick around too long, someone on the server is bound to notice that pink dot as an easy target.