Because you care about mathematical concepts and your daughter learning them, most likely she will learn them. You will point them out and talk about them. "see honey, you had one slice of banana, now, you have more slices of banana." You will be drawn to stories that contain math concepts (yes, they are out there) and games that teach mathematical concepts. When your daughter picks up a new concept well enough to apply it, you will notice and celebrate her accomplishment with her. All of these things are huge factors in helping her learn, but they happen more naturally than you might realize when exposure is occuring.
A baby's learning will be very concrete in orientation, as opposed to abstract as she is unlikely to be developmentally ready for abstraction yet. "and" is much more concrete than "or" so she is following standard patterns of growth in understanding well so far.
To help your baby learn the multitude of things she can start learning now, I suggest exposure without pressure Think of it this way, learning takes place because a child is exposed to stimuli, recognizes predictable patterns in that stimuli and responds accordingly. Babies are doing a lot of experimenting. "Last time I dropped this cup, mommy came over and picked it up. Will that happen again?" Now, it isn't quite that conscious in their little brains, but that is essentially how it works and why the do so many things over and over and over again. The key is to expose and then be okay with just letting the experience/idea/concept marinate in her brain and wait it out. Exposure allows her to use the concept and/or vocabulary as soon as she is developmentally ready for it, rather than being ready for it and then having to gain the exposure.
Ways you can support your child's learning in your home include
having things to count, talking about "a little" and "a lot/many" choosing story books to read that contain mathematical concepts, noticing sequences and patterns and pointing those out, comparing sizes (play games like lining up cups of assorted sizes in order from biggest to smallest) doing a lot of "sorting" (by shape, color, or size) and working with cause and effect - "Oh did you hear the loud noise the plate made when you dropped it? Will the same thing happen if you drop the plate again?" and generally encouraging experimentation and manipulation of objects.
I read Born on a Blue Day by the way! In regard to how your daughter's brain percieves numbers and whether or not she develops a passion for it and sees beauty in those numbers the way Daniel Tammet describes - I think that is one of those parts of the equation that is more nature than nurture or at least, unknown.
Having said that, the brain is elastic and mold-able - especially during these younger days (where your daughter is). Studies have shown that the structure of the brain of a child who learns music before five, is quite different than that of a child who does not (I'm sorry, I don't remember the reference to cite). This info is important to you because kids that learn to read and play music, also tend to do better in math and languages. Likewise, kids with tons of early exposure to written language and tons of stories at an early age, seem to be better wired for academic learning in general and tend to live more enriched lives down the road (partially because they have higher income - causality is difficult here).
I taught kids like Daniel Tammet would have been during his younger years if he had been diagnosed more accurately sooner. The school where I taught did a lot of in-house training and brought in researchers to do presentations etc. In my experience, we simply don't know a lot about the brain yet - let alone how learning takes place. What we have in knowledge in these two areas is increasing in leaps and bounds in the last twenty/thirty years or so, but the science is in its infancy so anything that one could do is still really in earliest theory stages (meaning they are little more than hypotheses at this point.
- Continue to love and be passionate about math and logic yourself - passions of the parents often rub off on the kids even when the parent tries hard not to push. That first paragraph in this incredibly long answer still applies here.
- Help your daughter explore everything you can allow her to explore - include music and storytelling as a component of every single day. Mathematic concepts show themselves in the most un-expected places sometimes so if she is getting exposure to a wide variety of things, she has more opportunities to make more connections logical or not between mathematics and the tangible world.
- Talk about how you see numbers and their relationships with her - some of it will rub off on her.
- Don't be disappointed if your daughter doesn't see math and its language the way you do, she has a loving father and she will find beauty and passion - even if it isn't in numbers. Isn't the most important thing that she feel fulfilled?
http://ponce.inter.edu/cai/tesis/lmrivera/cap2.htm goes over learning stages of cognitive development as represented by Piaget's theory (called constuctivism) and the psychological elements used within the process of learning.
http://www.assessingmathconcepts.com/criticallearningphases.html has a downloadable page that lists a lot of the skills teachers are looking at and measuring in Kindergarten upon a child's arrival at school - while I understand this is not the right "age" for this question, it will offer insight into what level is generally aimed for to be successful once it is time to start attending school.
Finally, http://www.education.com/magazine/article/preschool-math/ gives ideas on continuing to support the growth of mathematcal learning and conceptualization in your home as your baby moves from infancy into toddler-hood.
List of books for early elementary ages that present mathematical concepts and themes.
Hope this helps.