I applied for my daughter’s passport. Same day I registered her. Which was when she was one month. Took less than 2 weeks to come.( we are based in the UK) All I sent off was her birth certificate. I did it early because we went on holiday when she was 3 months. I even took the picture myself at home. Using my iPhone
We did ours 4 months before we travelled, it only took 2 weeks but both me & my husband had valid passports and somebody who was quick to sign off the identification part. I’d say apply after Xmas and get some extra time on it as the kids one is only valid for 5 years :)
You can do the passport now just so it's out of the way because you will need it when you book your holiday. I plan on getting my son's passport soon after I have the money. I think it can take up to three weeks if done online or longer by post.