My poor little fiddle leaf fig tree is struggling I'm watering it once a week and it's in indirect sunlight all day. The leaves are drooping and discoloring. I have one new leaf coming in, but it's the first new one in months. Do I need to re-pot in something larger? Any advice?

A couple things to check.
First, check soil moisture by sticking your finger in it all the way. Like most plants Ficus don't like having "soggy feet" (and are very prone to root rot) but when potted they need regular, deep waterings. So far all Ficus problems I have seen were caused by water: overwatering, underwatering (or no water at all), one inch of standing water in the undervase... If you have an undervase I strongly suggest filling it with gravel to avoid standing water and excessive moisture issues.
Second, tropical Ficus don't like temperature swings. That's why they should always be kept away from AC units, heaters etc. They also don't like sunlight extremes: I've found the best place for them in the cold season is about 7" away from a South facing window, while during the Summer they do well under a curtain.
But, again, I strongly suspect yours is a watering issue.

Finally, fertilizer... these are not plants that need as much liquid fertilizers as some websites say. They seem to be doing well with 2/3 doses a year, which can be avoided entirely if the plant has been freshly repotted. As I always say to people using too much fertilizer you should be growing cauliflowers and eggplants.

Thank you for all that helpful info! I'm including a picture of the bottom of the pot and the undervase...it seems the roots are coming out? Should I re-pot in something larger?

Roots get to the bottom of the vase, meet the moisture trapped underneath and the plant starts becoming stressed... a variation on the watering issue textbook.

You can repot in a larger container if you so wish, but check if it's not merely a case or roots having shot downwards, in which case you may get away with trimming the end of the roots and reusing the same container.
Three suggestions. First, if you intend keep on using containers with a single large drainage hole, put a piece of broken crockery over it. It will keep roots from growing through it but will allow excess water to percolate through. Second, put a layer of gravel or (second choice) sand on the bottom of that undervase... as a nursery owner once told me "Undervases kill more plants every year than chainsaws" . Third, repot indoors unless the weather outside is in the high 60's, otherwise you'll stress the root system even more.

Your FLF needs more light, not a larger pot. When indoors this plant requires lots of direct sunlight and soil that stays moist. If your Fig is still in its original nursery pot, it can easily be watered as soon as the surface of the soil is dry. If you repotted it and added soil to the top of the original rootball, you will need to remove that surface soil you added so you can get a better idea as to when it needs water.

It is very common for the roots of healthy plants to wander out of drain holes. It does not mean it needs a larger pot.