Here's one alternative. Using the data in your example
> do.call(rbind, lapply(paste("dat", 1:4, sep=""), get))
A B
1 1 0.02373546
2 2 0.03183643
3 1 0.04164371
4 2 0.06595281
5 3 0.05329508
6 1 0.04179532
7 2 0.05487429
8 3 0.05738325
9 4 0.05575781
10 1 0.04694612
11 2 0.06511781
12 3 0.05389843
13 4 0.04378759
14 5 0.02785300
15 6 0.06124931
16 7 0.04955066
17 8 0.04983810
For your full case use:
do.call(rbind, lapply(paste("dat", 1:1000, sep=""), get))