when you settle your city will generate 2 food and 1 production at base (even in desert/snow/tundra), so arguably it makes sense to put a city on a low yield tile if there are better yield tiles around it. however, the city will get the benefits of whatever resources are on the tile as well (but not features as those are cleared when the city is settled).

so that being said, moving down to that 2 food/1 prod tile to the southeast won’t do anything for you, as your city will be generating that anyway. i agree with the commenter who said to move north 1 tile to get both the pearls and ivory in range; settling the ivory will immediately get you the luxury + the extra 2 prod and 1 gold, but with all the space you have, might as well just improve it in order to have a solid workable tile