Swimming?

Can I take my 3 week old swimming in a pool? I live in the eastern area and its during this nasty heat wave, our house isnt fully air conditioned and were just a little warm! I wont keep her in the pool long, and we will be in the shade.. as we will go in my parents air conditioned house after maybe 10 minutes. Chlorine hasnt been added for 2 days. We though about putting water in the middle of the circular raft so shes not fully in the water but fully out either.