I've got a pakiT. I'm 5'4". They are available in 4 frame sizes and then BF customizes the seat height and the reach to the handlebars to fit the measurements you provide them. So, yes, the bike will fit you even though you are smaller.
As to whether the bike is going to help you with strong winds or steep hills, the honest answer is that is mostly dependent upon your physical conditioning. Having a lightweight bike and good gearing will help some, but you are the engine. If that commute is really a struggle for you,
you might consider getting the e-assist with the pakiT.
You've only been riding a bike for a couple months so I'm betting that you are not a very strong rider (yet). It takes time to build the core and leg strength to power any bike up hills and into strong headwinds. Since you already have the Brompton - unless you find it doesn't fit you well - you might be better off buying an electric assist for it and using that assist to help you until you get stronger.
I'm not trying to discourage you from buying a pakiT - I love mine and I love Bike Friday - but I don't think the bike is your issue. You might want to post in the electric bike forum here and ask about Bromptons with e-assist. Or maybe see if there's a shop near you that has e-bikes that you can try and see if you find the motor makes a big difference. Another advantage of the e-assist is you don't arrive at work all sweaty and gross, lol.