Could my 2 year old be gifted? What should I do?

People have been commenting on my daughters abilities. She’s 2.5 and speaks in complete sentences using complex words and ideas. I’ve seen this in others her age so I don’t know that this really means much. What I see that’s different is that she’s more advanced with anything with words and is really interested in writing, spelling and sight words. She can write a few letters, spells some words out loud and can read a few words without much effort from me. She just asks a lot of questions like what word is this and what does it mean and she seems to have a perfect memory to recite what she’s told. The most recent example is one where my mother in law was over. My daughter picked up a toy octopus and started spewing facts like an octopus has eight legs, octopus shoot out ink. She’s also told us that bats and owls are nocturnal. I don’t know where to go from here. Is this normal, maybe somewhat advanced behavior for this age or could she be gifted? There are no red flags for Autism or Aspbergers. Should I get her tested for giftedness ? Check out learning centers since she seems to really have a thirst for knowledge? Sit back and keep doing what I’m doing? I stay at home with her now and wonder how I can encourage her more. I don’t want to do something wrong and not give her the right tools or experience to flourish.