Dear Shaden,
There are a number of assessments available for use with very early childhood learners. I worked as a private educational consultant in New York City, and there is substantial use of some of these types of assessments when screening applicants to the private nursery schools and kindergartens in Manhattan and parts of Brooklyn. I simply caution you to be sure that you are always approaching these types of assessments with the intent to further foster the joy of learning in your little one, as I have seen too many parents approach very young children with unreasonable expectations and pressures to "perform" on these. However, given that you are on this site, I suspect this won't be an issue for you
Here is a link to a publication by the Pennsylvania Early Learning Task Force. If you skip to the end of the document, you will see a matrix with the names of several assessments, as well as what age ranges they are developmentally appropriate for.
http://www.pde.state.pa.us/early_childhood/lib/early_childhood/Early_Childhood_Assessment_For_Children_From_Birth_to_Age_%E2%80%A6.pdfAlso- in NYC private schools, they use the ERB assessments (ECAA/CPAA/CPLA). For more information about these assessments, check out
http://www.erbtest.org I know that in Manhattan there are people who work as full-time educational consultants, working with parents to assess their child's skills and areas for further growth- this is more or less what I did there, even with young children (ages 2-5). It may seem strange to some, but for parents that were not able to stay home and teach their own children, they sought out consultants to assess their children and foster fun learning activities with the children prior to/while in Jr. PreK/PreK.
I hope this helps! Feel free to message me if you have other questions!