The T3 to T1 will be somewhat new.. you may wish to cross post this on the Air Canada forum since YYZ travelers there will be more informed. I looked at the Toronto web page about transfers ...
http://www.gtaa.com/Index.aspx?Sid=N...ode2.7.3&Tpl=1 and agree it looks confusing.
I will not comment on the YYZ transfer as I have only arrived into Canada from the US .. and there is an 'in transit' feature within T3 that I assumed you could use .. tho with the transit to T1 it may not work. ASK about in-transit.
The luggage should not be an issue .. but again the transiting may be the problem if you have to clear into Canada and then out again.
The comment I WANT to make is more your JFK-YYZ flight. The new American terminal at JFK is not scheduled to open until mid August. Eagle flights all leave from T9 at JFK. T9 is notoriously BAD for security .. and BAD for lines .. and EXTRA sensitive metal screening machines (my belt NEVER makes it go off except at T9/8 JFK). AND be aware that parking and curbside dropoff at JFK T8/9 is HORRID. As international you MUST check your luggage inside at the ticket counter.
My point is allow PLENTY of time to check in at JFK and get to the gate. As a non-tier AA flyer you would not be able to use the VIP security line .. so prepare for some long lines. The Eagle gates are almost even with the security at T9 JFK.. you exit out of the security .. then actually make a 'U' turn like you are heading back out again .. and the Eagle gates are lower level on your right. DONT exit security thru the glass doors (with a security guard sitting there).
Your 12:25pm flight is the first flight on the 10th .. and the 7pm (next) will miss your LH flight .. so GOOD planning to have plenty of connection time in YYZ.
You do not mention a return .. be aware that you clear US Customs in YYZ before even getting to the concourse.... and the lines there (sometimes they have a US Passport only line which does not help you tho) sometimes VERY long. AND you take your luggage with you thru immigration and customs and then security. NOT a fun option.