We have one kid, one year old. Husband and I both work FT. As a result, our biggest change in expense has been childcare. Childcare is about the same as our rent, and I've heard a similar comparison from friends who live in other areas with lower cost of living.
Most gear you can get used/hand-me-downs in the baby and early toddler stage. We have spent zero on clothes/toys.
Food is starting to get a little more expensive as I do think it's important to offer baby some variety in his diet, but I would say the "extras" are <$20/month.
We did a bunch of meal prepping and made a load of dehydrated meals before the baby was born. I'm pretty sure this has saved us a ton of money as we haven't really felt the need to get takeout or meal delivery or eat lunch out during the week more often, both things that friends with babies have reported doing often.
One area we did start spending more in was utilities! We do laundry a bit more often ($5-10/month more), and we also found that our baby slept better during the winter if we used a space heater to keep the temperature in his room around 65F, which has added $20-$30 to our electricity bill.
I think the big difference for us pre- and post- kid is that time is at MUCH more of a premium than it used to be. So if any of the stuff you currently do to stay frugal is very time-intensive, you may want to expect to have to replace that with a more expensive alternative.
Finally, are you thinking you will have a SAHP or both continue working? I think one thing people think about having a SAHP is that your childcare costs will be zero, but that can be quite constraining for the SAHP. If I were SAHPing, I would still want to have some money in the budget for activities (e.g., mom&baby classes, perhaps going for coffee with the other moms after class, etc), and an occasional babysitter or 2-3 mornings a week at preschool once the kid was a little older. You should also consider whether or not your current living space is really "okay" for having a SAHP. Our apartment is kind of small to be home for all/most of the day with a baby or toddler, so if we had a SAHP I think we'd want to move into a larger, nicer, more expensive place.