Some other guide tell you in general but to be more specified here's exact thing to do to get Fishing Rod from Loretta.

You have to complete Bad News quest (Share the news about Liam with the rest of Barrenpyre).

Once you have that completed, speak to here again and again (in my game it was after 2 tries) and she open new dialog starting with What's up? where she tell you to use her old Fishing Rod to fish for her on her dock.

That open new quest in Friendship Quests called: Fishing for Something quest (Go fish by the Barrenpyre Beach).

If you haven't fish yet, here's how: Walk to fish spawn spot near where you are, press E to throw Fishing Rod and start fish.

PAY ATENTION NOW!
Once you have shout marks (exclamation mark) [!][!][!] - IMMEDIATELY PRESS LEFT MOUSE BUTTON to pull Rod out and you will catch a Book called "Angling across the pond", which will appear on deck, next to you.

Pass that book to Loretta and that complete this quest.

Once you hand her a BOOK she tell you to keep Rod (drop one in your hand as this particular one is hers).

Your own Fishing Rod is in your Tool Storage.