for as far as i know, the time at which the letter comes depends on the time your tama grew and in the pausing behaviour. if you put it on pause, it will take longer for the letter to come.
Also, some persons got their letters very quick, others some time later, so there seems to be quite a time span in this.
If you are new to a v4, you may not know that you get a letter soon afther transforming in to a toddler, When you go onto tamatown, yours may be a toddler , but you may of not got the letter yet, it looks like this, [!]
If you havent and you are on tamatown, then you wont be allowed into preschool...
You need the letter to get into preschool so even if your Tama's a toddler and it won't be able to go to school until it is accepted. Now you said on TamaTown that it appears as a baby when it's a toddler. Could just be a TT error. Logout and log back in.