Oh no, she's not ready to drop the nap!
I suspect she's just ready to increase A time a bit. If she wakes at 8:30 and goes down for nap at 12:30, that's only 4 hours of A time. Pretty short for this age, which should be closer to 4.5-5.5 hours of A time. My guess is if you change nap to 1:30, she'll go to sleep faster. What happens when you put her down to early is she plays ('cuz she's a toddler and that's what they do!
), and then overshoots her sleep window so plays and plays and plays and has trouble winding down.
The sleep troubles with new babies have to do with emotional insecurities in toddlers. They worry that mama is having fun with little one, or that mama won't be there for them now that another baby is there to take up mama's time, etc. If you're not seeing any other SA or insecure behavior, I'm guessing you just need to increase A time. Try 4.5 hours A time first and see how that goes. Increase by 15 min. each day until you see her napping better.