The couple, who are set to wed in a “not too fancy, very laid back and cool” wedding later this month, didn’t plan this overlapping of events, but Jane says that it was a happy coincidence: “[Alex] asked me to marry him and then I found out that we were going to have a baby. The baby wasn’t planned exactly, but our future was. It was going to be in there somewhere, we just didn’t know when.”

Jane also tells ET Canada about how excited her parents are about becoming grandparents: “Both my parents are so excited, they keep calling me and they’re like, ‘I can’t wait to have a little rugrat running around the house.’”

From singing lullabies (”He can be crying at the top of his lungs and just turn off like a switch”) to frequent bottle-feedings (”I’ve never seen a baby eat like he does!”), the singer (who chose not to address the tragic loss of her family members last October) offers PEOPLE an intimate look into her new life as a mom.

How hard was it keeping your pregnancy under wraps?
“David and I were the only people who knew for a long time. I would forget I was pregnant, it was so easy. I didn’t have any morning sickness, no cravings either. I just thought, ‘Oh, well, we’ll wait until it’ll tell on itself.’ I didn’t show until I was seven months so that made it easy right there.”

Your son was delivered via C-section, what was your recovery like?
“Everybody told me how much it was going to hurt afterwards but I think I have a different tolerance for pain than others. By that night after I had the baby, I’m like, ‘Look, I can’t sit in this bed anymore. I’ve got to get up!’ I’ve been up and about since he was born. To me, the pain is no different than when you work out a muscle you’ve never worked out before and it’s sore.”

Has his personality emerged yet?
“He has a lot of personality, like David. He’s always been a good sleeper. His favorite time to smile now is diaper changes. Or when he spits up on you – he just cracks up like he thinks it’s the funniest thing. And his bottle is his pacifier. With a pacifier, it’s like he knows, ‘Ain’t nothing come out of here. No, I don’t want that. Where’s the real deal?’ His best friend is that bottle; that’s all he wants.”

Would you be supportive if he wants to pursue a career in entertainment?
“We’ll definitely encourage education. His father is an education fanatic so we definitely want him to get an education and go to school. My mom always said, ‘Whatever you want to do, I’ll support you as long as you’re happy.’ So I will do the same.”