You're going to love it
It does work outdoors - I'm brooding chicks out there right now with it in a cold VT winter. It is smaller, but it sounds like you wouldn't need the bigger size anyway and it has a lot of good points to it too.
For example it uses a lot less power than a heating pad does, it's very easily adjustable whereas using fence etc for a frame for the heating pad really isn't as easy to adjust as the heat plate is, unless you build something like aart's nice design but that costs more money unless you happen to have the supplies around. Plus there's no danger of a chick getting caught between the frame and the heating pad and dying like I've seen happen with the MHP method (although that can be fixed with further modification to prevent such a thing happening). And it's easier to clean than a fabric heating pad if the chicks soil it - a quick rub down with a damp cloth and you're good to go, no need to cover it with a pillow case or something and then do laundry after.
I feel you about it being hard to find a cheap heating pad with no shut off - the one linked in the heating pad thread that is recommended costs $40 on its own. Pus the other cheaper one in here that was linked says it has no auto shut off, but if you read the reviews it actually does have one after two hours, or at least some of them being sent out do, so that might not have worked for you anyway.
Anyway, don't feel bad about buying the heat plate or like you wasted your money or anything - while MHP is good, the plate does have some advantages over it in some areas, and I think you'll be happy with it.