The first answer is on the money (BTW quaver = 8th note, semiquaver = 16th note). His or her advice is based on sight readers wanting to clearly see the beginning of every beat (in this case beat 2 of each bar) when 16th notes are involved. You can also substitute a single dotted 8th rest for the 16th and 8th note rests if you like.
If you want to compare one which has very little pedal, have a listen to some of Glenn Gould's recordings. For example this one:
The same fugue starts at 15:10 on the Richter recording you've provided. You will see that the difference in pedal usage is pronounced.