If your value of $n$ is small, but not so small that you want to go through a list of knots and links by and, an alternative is `plantri`: <
This is a C program that will generate a list of planar graphs with certain properties, depending on the input. In your case, supposing you want graphs on $12$ vertices, you could use
plantri -p -m4 -c1 -e24 12
where `-p` asks for general planar simple graphs, `-m4` asks for graphs with minimum degree $4$, `-c1` asks for graphs with minimum connectivity $1$ (connected graphs), `-e24` asks for graphs with $24$ edges (together with the minimum degree condition, this implies that the graph is $4$-regular), and `12` asks for $12$-vertex graphs.
(In general, for $n$-vertex graphs, you will want the `-e` parameter to be $2n$.)