I'm in the same boat as KC , when it comes to saying exactly what mat'ls have been used in building your table .
I do think that the design was a bit more thought out , as far as symbolism in the inlays , than alot of currently produced tables of this type .
When peacocks & peonies are depicted together in/on Chinese items , generally they stand for 'Fortune & Longevity" (or other positive variants) .
When peacocks face each other , it typically represents a symbol for 'the duality of all things' .
Lots of work went into the inlay on your little table (time is money) , so there's that...
If you do dare to , perhaps you could do a "red-hot needle" test (in an area where you'd have to tolerate the small damage , if it's synthetic) on the suspected MOP (Mother-Of-Pearl) material .
If the red-hot sewing needle does not melt the mat'l , it's probably shell of some sort .
It's not unknown to also use other types of shells -oyster,etc.- for such inlay work .
IMO , the MOP mat'l , if that's what it is , was either dyed or painted (in a couple of areas) - if it's been painted , do be careful if you're thinking about refinishing it .
I think it's possible that your table may be signed , somewhere hidden (or obvious) .
BTW , welcome to the forum , cristalm88 .