School's Almost back in: Age is just a number

I teach first grade. I know children of this age range do not have any concept of time. I ask them how old they think I am (34)and I get answers that range from 62 years old to 16 (those are the kids I give the A's to). But yesterday's conversation between Ava and her friend made me want to submerge myself under the pool water for a long, long time, perhaps 62 years, and possibly even rethink my career.
Ava and her friend were playing in the pool with a doll that can go in the water. Her friend Abby had the doll on the raft and said, "My baby can't go in the water because she's only one month old." Ava says, "Oh."
Long pause, "How old's your baby?"
Abby: "one month."
Ava: "Yeah, but like, how old is she?"
Abby: "She's one month Ava."
Ava: "Abby, you're not understanding me, I want to know how OLD she is."
Abby: "AVVVVVAAAA, I told you she's ONE MONTH."
Ava: "I know she's one month, but that's not my question. I want to know how old she is, like I'm 6 and you're 7, how old is the baby?"
Abby looks to me for help. I say, "Ava, the baby was born, then turned one week, then two weeks, then 3 weeks, and then a month. Babies are one month and then two months, and they have to be 12 months old and THEN they start counting by years, they are one year old, two years, old, etc. So this baby (mind you, I'm referring to this inanimate object who's floating upside down in the pool at this point - I think Abby was trying to ditch the thing so Ava would forget about it already) is not 6 years like you, it's only ONE MONTH old. It was born in July and now it's August. It's a little newborn baby." Whew, that outta clear things up.
Ava: "Mom, you don't understand my question, I just want to know how old the baby is. I'm six years , Abby's 7 years, how old is the baby?"
Me: "She's zero ok? Zero years old Ava." ("patience is a virtue, patience is a virtue" I say in my head)
Ava: laughing, "Mooooom, no one is ZERO years old!!!! Just tell me how old the baby is!!!"
Abby and I exchange looks....she tries to explain it, I try again to explain it. This exchange went on, and on, and on....it was seriously like "Who's On First." I thought (hoped) that at any minute someone was going to jump out of the bushes and tell me to "smile" because I was on candid camera. No such luck, I had to pay Abby 5 bucks and a Popsicle just to say her baby was 2 years old. (crap, I promised a long time ago to tell only true stories huh?) No money, just a Popsicle, but it does the distraction trick every time.