The dog we have now was completely sheltered and had never been outside so was afraid of anything and everything that moved. And we got her about a month before Halloween in a neighborhood that goes all out with decorations. If not for getting 'quite old' like you say, it was almost funny at first as her response were so skittish and jumpy to birds, airplanes, cars, rabbits, kids, bikes, bad weather...then came the scarecrows, and pumpkins...
I never even thought of hiring a specialist like suggested below. It just didn't occur to me. My approach was constant exposure to help teach her normalcy. I role modeled confidence to her. I would tell her in a happy, positive voice what she was seeing and reacting to, using her name and strong eye contact.
I would recommend you sit on a lawn or grassy area and just play with her under the open sky. I don't recommend walking, b/c that will make her feel like she's on duty and needs to be protective and needs to be 'on watch.' Just sit and pet her, stroke her, play fetch, have a few treats nearby, then when a plane approaches, tell her in a happy, confident tone, 'Oh, look Doggie's name, a plane, a plane, yeah a plane.' Smile big like you are really happy about it. Rub her extra in her favorite spots too.
The other helpful item for us was we rode our bikes to school and I put her on a leash and she had no time to react to all the scary things. She tried to in the beginning, but the bike just kept rolling and she'd have to keep up. I think the bike ride made her learn to forget about it quicker and move forward. Because I was not stopping for her scaredy cat reactions while on my bike.
Hope something helps.