Birders! Question

I have been watching a bird that feeds at the seed feeder coming and going with pieces of grass and twigs in it's beak and assumed it was building a nest somewhere near. Only thing is, I didn't realize how near. I saw it pop into a flower hanging basket and come out sans grass and twigs. OMG no way is it building a nest in the planter. Well actually yes, I found an almost completed nest inside the planter and I knew I had to get rid of it quickly. With 2 dogs and a cat those babies wouldn't stand a chance. So reluctantly I took it out and threw it away. My question is...does the bird have time to build another nest somewhere before eggs come?

Last year I had a traumatic bird event while weed wacking alongside the house when I hit a birdnest with mother and babies. That did me in for a while and I didn't want to go through that again.