I wouldn't get a Kindle Fire for a 2yo! We have one, but I got it when it was £35 quid on Amazon as an impulse purchase and didn't even open it for six months. DH reads Brexity news on it in the loo so I prefer not to touch it (yeuch! What is it about men and reading tablets in the loo?) and certainly wouldn't let DD near it.
DD is nearly 4 and doesn't use a tablet. I work in education (in an area that bears on media theory!) and see no need to give her one purely because "that's where life is moving" or "they have them in schools". These are not technologies that will teach your child much: they are passive and designed to be so, like watching TV. (MY DD watches entirely too much TV, I have to say, but does loads of non-TV play too.) Books, drawing, playdoh and outdoor play are all much more interactive than tablets: don't be fooled by the "interactivity" that is built into them: it's designed to offer you only very limited ways of interacting with the device. It will teach you nothing about how digital devices work or how to understand them or indeed to make or code them. They are designed to be "intuitive" and hide their interfacing behind a spurious naturalness, offering you very scripted pathways that feel natural but are very limited. They are also designed to be used by someone with little to no experience of the digital world. They are a very limiting way in to technology.
My own students (aged 18-25, from undergraduate to PhD) have all grown up as digital natives whereas I barely used a computer before the age of 18. I am actually now far more at ease with the digital world than my students are and much more able to make use of new technology. I was very puzzled by this until I watched them closely interacting with technology in seminars, etc., and ran some detailed hands-on classes on digital resources with them. Their problem is that they don't really understand the underlying ways in which physical knowledge and conceptual data are organised - they don't really understand the organising principles of library catalogues, databases, data sets etc. Neither do they know or understand anything about Boolean searches or how to access and evaluate digital information properly. This means that they tend to treat the digital world, and especially the internet, as a kind of floating morass of "information" that they blindly type phrases into and then see what appears. They expect programs to give them pat processes and answers rather than understanding how to manipulate data fields and sets. In short, they appear genuinely bemused by a sort of undifferentiated fog of information that they are not sure how to navigate. They are also attached to their tablets, phones and laptops like their life depends on it.
If you want your toddler to be well-prepared for school and life, give the child some books; take her to a library and explain how it works; get down on the floor and help her build some small world play environments so she can develop true skills of concept-building and analysing the structures of the world around her. A tablet is like TV: pure entertainment but don't kid yourself that it is educational - it isn't.