Could you use 모으다 here or is 줍다 more natural?
모으다 is more for saving things, where 줍다 is more like picking it up to collect it.
In a more natural-sounding sentence, one might use the verb 따다 instead of 줍다 (imo)
줍다 is not the correct verb for "gathering" strawberries. It is used for gathering nuts that are picked up off the ground. 따다 is generally used for harvesting / picking strawberries.