Jon, good to hear you've found a suitable gas dryer.
It would be interesting to see pictures of your electrical installation. The smaller Square-D brand box is likely newer. If the wires from the meter go into it directly, then into the other panel, it is the main disconnect. Are those two fuses round that screw in (plug type) or long that fit in clamps (cartridge type)? Also, if pulling down that handle turns off everything in the house, it is the main.
Since your house was built in the very early 1900's, there is the possibility there may be other fuses located in odd places in other parts, such as the attic. This is common especially in larger homes with two or three floors. My cousin's house had multiple fuse locations; some were just porcelain fuseholders screwed to framing in unfinished locations. Another was on a pantry ceiling. Once it took them hours to find a blown fuse.
Regardless, I'd get an electrician to verify that you don't have any fused neutral circuits. They are a shock hazard if the fuse blows in the neutral side, but not the hot. This makes it appear that the circuit is dead, but it is NOT.
If you're planning to stay in that house long term, you'll eventually need to do something with the wiring. Since having an electrician is so costly, you might consider taking a course at a vocational school to learn how to do it correctly, and therefore safely. I did that back in the 70's. It was money well spent.