Thanks, Allison!
Yes, you have 4GB. The first report shows each of two RAM banks (slots) separately. 2 + 2
For RAM I'd try is seeing if Crucial offers a NZ site or allows you to use the UK site.
I found this but have no idea of their reputation:
https://www.upgradeable.co.nz/apple/MacBook_Pro/MacBook_Pro_2010_(Mid)_Core_2_** o_2.4Ghz_13-inch
My only concern was that they show a 16GB option for your computer. Then I looked at my preferred US RAM vendor, OWC< and see that for the MacBook Pro7,1 they also show a 16GB option specifically for the 7,1:
MacBook Pro Memory Upgrade Kits (2008-2010)
Upgradeable's contact info shows they are also a RAM manufacturer (in Oz) as well as a reseller, and all their solid-state drives appear to be Crucial brand. And they confess to being Mac users. From one of their pages:
Everyone at Upgradeable is a Mac user, we own Macs, we love our Macs.
Could be good.
I don't think you need 16GB. My 2012 13-inch MacBook Pro (same family as yours) has 8GB and has never "run out" of RAM according to both Activity Monitor and Etrecheck. If 4GB seems too little, I think 8GB would handle all you need unless you use the computer to do seriously heavy-duty pro apps.