"do kumquat trees need to be planted in the ground?"

They do equally as well in both the ground and a pot.  If you want to move your tree into a pot, wait until after it has finished fruiting.  Prune it back as you would at the end of every season, then dig it out leaving a root ball that extends to the drip line.  Repot it using a quality assured potting mix, and a handful of blood and bone mix that is mixed in well with the new soil.  Make sure you back fill the new soil to the same level that the trunk was in the original soil.  If you fill it too low, the roots may become exposed as the soil subsides, or if it is too high, your tree may die from collar rot.  Once you have watered it in, making sure not to drown it.  You should not need to fertilise beyond the blood and bone added earlier, as you could burn the roots and kill the plant. Only water if the soil is drying out until the new growth starts for the next season.  It should do very well in a pot so long as you keep it well watered and fed.  You can use a citrus mix once the flower buds have become new fruit.  A couple of times during the fruiting season, sneak out under cover of darkness and pee into the pot.  This may be hard if you're of the female persuasion.  Urine contains phosphates and ammonia that citrus trees love.  Just don't tell anyone when you give them some of the fruit.

Kumquat trees are slow growing members of the citrus family. Some varieties reach 9 feet tall, others such as the kumquat Hong King are shrubs and can be potted. It is important to know which variety you have. My in-laws have a very old heavily fruiting kumquat tree. It is about 10 feet tall with about a 6 foot canopy. They never do anything to this tree but water it and prune out occasional dead branches.

 

Here is what I found on potting up kumquat trees:

 

In orchard plantings, kumquats on trifoliate orange can be set 8 to 12 ft (2.4-3.65 m) apart, or they may be spaced at 5 ft (1.5 m) in hedged rows 12 ft (3.65 m) apart. For pot culture, they must be dwarfed; must not be allowed to become pot-bound, and need faithful watering to avoid dehydration and also need regular feeding.

 

I'd give it some time if you are unsure whether this a shrub or dwarf varity before moving it.