At the time the screenshot was taken, the city was 2 turns from going to size 7. Even at size 7 and no other irrigated squares it will still have a decent food surplus and get to size 8 pretty nicely. Since it already supports a settler (wherever it is) and has decent commerce, it can surely benefit from a library right now.
While irrigation will be nice after an aqueduct is finished, if we do get a settler there I think a priority should be roads to boost the commerce further.
And let's get that silver caravan delivered!!!
I'd like to suggest that we not wait too long to get another caravan made here as well. Once the library is finished, the silver caravan delivered, and some roads built then a second caravan could be very profitable indeed!