My girls love math as well, and we do "math quizzes" by request in the car most trips. They also love math "tests" I make for them, though they request them more now that they have learned to write. Be aware of this, it can often be mistaken for reluctance.
One thing I love about making our own math sheets is being able to tailor them to what is wanted and the proper level. I'm able to ask them what was easy, boring, hard and fun or hard and frustrating, then I make a new one based on that. I like that they can request addition or multiplication or division, even though their grade levels stay at addition and subtraction. And they only cost 1/500 the price of a ream of paper--or cheaper if they are on the back of scrap paper.
I think it's fine to play with written math at this age, but one of the biggest favors you will be doing for her is to continue pointing out that math isn't just what's on paper. Maybe you want some new vocabulary for math done on paper to help this along. Then to preserve her love of it as long as you can, let it be at her request--both to start and to stop.
My friend just introduced me to a fun activity that my girls were excited about--for a minute at least, but their friend loves it: paint one side of a few beans, then toss them and create an equation from the beans. 8 sides painted+ 8 sides plain= 16.
My girls also loved exploring the calculator. I can't count the number of times I've heard "Mom! 15+15=30!!!!!!!" Their little video games helped them add by tens, hands by 5's.
It's wonderful to see kids so in love with all things math.
We love Anno's Math Games, but those 3 volumes are slim on counting, more on concepts, but the presentation is wonderful and it is a good read anyway. Recently we had some books by someone or other that the girls enjoyed, but I can't think just now. I'll try to remember and get back to you.
Have you asked her what she means by "learning math"?
I'd find out, more specifically, what it is she wants to learn. If she can't say specifically I'd go with a few examples of things she might like learn to do (learn to pay for things in the shop, learn to tell the time, learn to count and take away, learn to play Snakes and Ladders) and see if any enticed her and go with those.
I'll be honest, I wouldn't make too much of it really, I'd keep bringing it into daily life. In the example you give, her learning was very firmly rooted in her family, in emotion. I'd keep it very, very concrete and o at her pace. I wouldn't buy a book yet, but if you really did want to I'd personally recommend Miquon.
Really and truly, I would not rush to get her sat down doing worksheets or workbooks. At the end of the day, you want her to have a great, concrete foundation for later maths-which is what she was doing for herself in your example. You are NOT going to get that by just starting her on a workbook, aside from, possibly, something like Miquon (montessori-ish) but with a LOT of extra fun stuff thrown in. I'd keep on with what you are doing tbh, as its obviously working!