Assuming you want to match the whole line with your pattern, this works:
sed -n '/^dog 123 4335$/ { s///; :a; n; p; ba; }' infile
With the following input (infile):
cat 13123 23424
deer 2131 213132
bear 2313 21313
dog 123 4335
cat 13123 23424
deer 2131 213132
bear 2313 21313
The output is:
cat 13123 23424
deer 2131 213132
bear 2313 21313
Explanation:
/^dog 123 4335$/ searches for the desired pattern.
s/// empties pattern space, assuming you do not want the pattern included in the output.
:a; n; p; ba; is a loop that fetches a new line from input (n), prints it (p), and branches back to label a :a; ...; ba;.
Update
Here's an answer that comes closer to your needs, i.e. pattern in fil2, grepping from file1:
tail -n +$(( 1 + $(grep -m1 -n -f file2 file1 | cut -d: -f1) )) file1
The embedded grep and cut find the first line containing a pattern from file2, this line number is passed on to tail (+1).
Note that not all tails support the plus notation.