I work almost exclusively with an EI population. Biggest differential DX in this age group is going to be between ASD, language disorder, and global delays in development. Also important to identify the extent to which cognitive delays might be impacted either (hint- they probably aren't, but you should check anyways!). For standardized direct tests, i use the Bayley-4 Cognitive and Language Scales, and will occasionally do the Bayley-4 Motor Scales if indicated, largely to get a baseline and aid with identifying/ruling out more global delays. I use the criterion referenced ADOS-2 (be sure to get REAL training, including on the Toddler Module). For parent quenstionnaires, for kiddos up to 2-6 I use the Bayley-Social Emotional Behavior Questionnaire (if kiddo is older than 2 and ASD is not primary rule out, I may use Vineland-3 and Behavior Assessment Scale for Children (BASC-2). Kiddo's older than 2-6 I use the Vineland-3 and the Social Responsiveness Scale (SRS-2). If there is any chance that you will be seeing kiddos older than 42 months (max age for Bayley Scales), you'll also need a preschool-primary aged cognitive battery, like the WPPSI-IV or Stanford Binet, as well as a language measure (If language obvious very low, I use Preschool Language Scale (PLS-5), if they are taking more, I really like the Comprehensive Assessment of Spoken Language (CASL-2), as it really does a good job of identifying between kids with a good receptive-expressive vocabuary for words who have difficulties with more complex language abilities (e.g., graphical morphemes; sentences; pragmatic language).
You should also be informed enough about traits related to more common genetic conditions to know when you should definitely refer to to a developmental pediatrician or neurologist. Most general pediatricians are pretty comfortable with ASD, so when I diagnose it I will typically direct families to inform the pediatrician and have a discussion about the need, if any for additional referrals. If I get a kiddo with potential signs of genetic or medical conditions (e.g, hallmark facial features; over 18 months and not waking), who the general pediatrician has not looked into a little bit more, I STRONGLY recommend the family ask for referral to a developmental Ped or Neurologist.
As far a salary expectation, EI assessments can work different in every state. In MA, where I am, the assessment needs to be done by a licensed psychologist health services provider or a pediatrician to qualify the child for insurance reimbursed ABA services (though there are some exceptions for kiddos in EI who are awaiting a more formal assessment). In CT, a Licensed Worker can do the assessment for EI (called "birth-three" there), and does the assessment in the child's home (!), but that won't qualify kiddo for after 3 ABA services for ASD. You mention you are a licensed school psychologist. Are you licensed at the doctoral level as a health services provider (or NY equivalent)? That will definitely impact salary range, as will experience, additional certifications (e.g. BCBA), other things you can offer the agency. Expect a lot of medicaid clients in EI.
