There is nothing on the TSA website or Southwest that would prohibit you to carry on knitting needles. However, there is a section that states any metal item with a sharp point are not allowed on carry on but can be placed in your checked luggage. To be on the safe side I would place them in your checked luggage.
SWA Guy is spot-on with his recommendation. As an extra reference, here is the excerpt I found pertaining to knitting needles & other needlework items from a helpful web site; www.tsa.org.
"Circular thread cutters or any other cutter or needlepoint tools that contain blades must be placed in checked baggage. You are permitted to keep scissors smaller than 4 inches in your carry-on baggage.
Even if an item is generally permitted, it may be subject to additional screening or not allowed through the checkpoint if it triggers an alarm during the screening process, appears to have been tampered with, or poses other security concerns. The final decision rests with TSA on whether to allow any items on the plane."
Since TSA guidelines are ever-changing, I highly recommend consulting that site prior to taking any flight, or to check on specific inquiries like yours. Warm, fuzzy knitting & happy, safe travels to you!