Unless you are aware of a potential delay, I would not do the ASQ every month....I would aim for every 6 months or so if you are worried.
Growth and development can come and go in fits and starts, so what looks like a delay may not be a month later. Often LDs have to be a 6+ month term difficulty (as well as for an identified 'delay' for all but infant/toddlers).
Many kids may show a delays and then catch up or be on track for awhile and slowly fall behind developmentally.
FWIW-- both my DDs had delays from birth to age 3 for one and one still has mild delays (just about age 5). The older she gets the 'less' it is apparent and the more gains she is making. Both of them seem to be very bright- but one has some gross motor/social delays.
LDs are not usually identified until after age 6 / 7 or so for developmental reasons- there is a wide wide range for normal at those ages. LDs are often show too as a discrepency between ability (IQ) and achievement....IQ scores are not considered very accurate until age 6/7/8+. Yes, kids under age 7 get them, but they are not terribly stable for the preschool set. Though a highly gifted child will most likely stay gifted, but for LD purposes----testing and identifying LDs would be very very difficult at that age.
LDs can present in reading, writing, math, or non -verbal LDs. So focusing on reading is not always the best indicator.
Usually the schools will not test a child for LDs until they are in 1/2nd grade and showing academic difficulites. First they do interventions (title 1, reading support, etc)...then they will often refer a child for testing (or a parent can) if interventions do not seem to provide remediation.
LDs can run in families or not- I found it to be only a mild factor---though there are some kids I worked with that had family history (siblings parent). They are exhibited in all populations (gifted , bright, standard students, and students with cognitive impairments). They can also be statistically increased in students that have other difficulties- ADHD, prenatal drug/alcholol, TBIs, etc).
Speech has a correlation with LDs, but it is very low. Lots of students have speech/language therapy and never need or qualify for LD support (and some LD students do not get speech services).
I would not worry about a 2 yr old unless you are seeing huge delays....family history regardless.
From age 2 until K/1st grade or so, it is unlikely that you will see students getting LD services. Some students that age get OT or PT (fine and gross motor) but before actual elementary age, LD are rarely even tested for.
You can get tested through the schools after age 3 if you have any concerns and get OT/PT/speech/etc through the schools if there is a delay.
Before age 3- Early Intervention could help and offer the same services.
For evaluation, privately it is expensive--but local colleges and/or educational psychologist could do an evaluation.