b1 b2 to h1 b query

[mehta]

I have a query . I currently hold a 10 year multi entry B1 B2 visa . On my last business visit to the US I found an employer who has offered me a job and an H1B VISA . I am in my native country currently and my employer has advised me to arrive in US first week april on my current b 1/b2 and then apply for an AOS once I am here . He plans filing the H1 B petition for me in 2nd week april . But I can see in some of your replies that one should have been in US for atleast 2 months before applying for an AOS . I am currently in another assignment and cannot travel before 15th march .
Would the quota be exhausted by say 15th may ?
can my employer file petition a couple of weeks or a month later when I arrive (as he plans ) ?
I also have a multi entry canadian tourist visa . can I opt for change of staus and visa to be issued abroad (in canada ) ?

please help . looking forward to ur reply