Yes, get the Off Camera Shoe Cord. Or an ST-E2 (for 580EX, etc.) or ST-E3 (for 600EX). Wireless control with the 6OD won't work with the 600EX and with other flashes it won't allow you to do rear curtain sync or high speed sync (FP flash). Plus, it uses pulses of the built-in flash to communicate with the off-camera flash, so the flash has to be in front of the camera within a limit arc of about 80 degrees. Likely a bad place or the flash, taking a macro shot (actually it's one of the problems with the IR controlled flashes for non-macro shooting, too, that the flash has to be in front of the camera to work, though using and ST-E2, which can be pointed to the side, can help).
You don't need the 600EX (unless you really, really gotta have radio wireless control for other reasons). In fact a smaller flash such as 430EX or even 270EX might be a better choice for macro, yet still be a pretty good "all purpose" flash.
The "best" flash for macro specifically is arguably the MT-24EX Twinlite.
But the MT-24EX is pretty much a dedicated macro flash.
Another dedicated macro flash is a ring light, such as the MR-14EX. Personally I'm not a fan of ring lights with typical macro magnifications up to 1:1 or a bit more... Though they are fine with higher magnification (2:1 through 5:1). IMO, ring light give too flat lighting effect at the more modest magnifications. That makes for rather scientific looking images, perhaps good illustrations of coins or watch mechanisms, just not very "artistic" light modelling effects and less three dimensionality.
A single, standard flash such as the 580EX or 430EX works pretty darned well, too. Nice because it double to use as a regular flash for other purposes. And the easiest way to use it is with an off-camera shoe cord.
Often with a standard flash such as the 580EX II in the photo above, the output is too much with a close up subject. However, a simple solution is to attach a couple layers of white qauze bandage over the flash tube, to act as a diffuser and reduce the output, as shown. That's what was done for this shot..."I'm ready for my close-up, Mr. DeMille."
EF 100mm f2.8 USM macro lens at f11. EOS 30D camera at ISO 100, 1/200 shutter speed. Handheld with 550EX flash, off-camera shoe cord.
The reason a single, standard flash works is that it's sort of like a giant softbox, compared to a small macro subject. The light tends to wrap around the subject, for pretty nice modelling even with a single light source. If the critter is slow enough moving or cooperative enough, you also could use a bounce card, to fill the shadows a bit, if you wish. That's in lieu of having a second flash (though one or more could be triggered by the main flash, in a Master/Slave arrangement, without the limitations of the camera's on-board wireless flash control.)
There's another problem, though...
WIth an 18MP camera such as 60D, you are going to start bumping up against diffraction as an issue, trying to use really small apertures. Your lens can do f45, but due to diffraction a lot of fine detail will disappear from your images. With an 18MP, crop sensor camera, the Diffraction Limited Aperture (DLA) for an 8x10 print is f7.1. A camera with a less crowded sensor with larger pixel sites can tolerate a smaller aperture with less diffraction effect... a 21MP 5D Mark II's DLA for 8x10 print is f10.
The DLAs mentioned above are the apertures where diffraction starts to occur. It isn't bad, has pretty limited effect at first. So I'll use f11 without much concern on my 7D (same sensor as your 60D), and sometimes even f16. But with each smaller aperture, diffraction and loss of fine detail increases. So I try to avoid apertures f18 and smaller, with an 18MP crop camera.
So, as suggested above, you might want to look into focus stacking... the difficulty with that is you have to make a series of shots at slightly different points of focus, to combine for the final image. It's possible when shooting a stationary subject, but moving subjects present a challenge to make a series of shots. (An old bug photographer's trick is to refrigerate your subject for a 15 or 20 minutes before the shoot, which will immobilize them for a few minutes... of course you have to be careful not to kill them in the process! Alternatively, shoot outdoors on cool mornings, before critters warm up and get active.)
Shorter focal lengths will have more depth of field than longer ones at the same aperture. Here is an image shot with a 180mm macro lens at a middle aperture (unfortunately the exact setting was unrecorded). You can see how DOF is just a couple millimeters deep...Golden bee
EF 180mm f3.5L macro lens. EOS-3 camera with Ektachrome E100VS or E200 film. Settings unrecorded. Handheld (camera and lens resting on the ground). Available light (no flash).
There's some subject movement, due to a breeze, but the image below was made with a 20mm lens with a 12mm macro extension tube behind it. That very wide lens was used to gain a lot of depth of field, retain much more background detail than is usually possible.California poppies
EF 20mm f2.8 lens with 12mm macro extension tube. EOS-3 camera, Ektachrome E100VS or E200 film. Settings unrecorded. Handheld, available light.
At times when trying to shoot the above, the petals of the flowers were in focus when touching the front element of the lens. That's the down side to using a shorter focal length to gain DOF... you lose working distance, too. It might be okay shooting flowers that way (just watch out for accidentally casting shadows on your subjects), but usually you have to maintain more working distance with skittish insects.
It can take a lot of tries, to get one or two good macro shots. I think I took about 75 shots of this bee, to get a couple I was happy with...Bee on orange poppy
Tamron SP 90mm f2.5 macro lens (vintage, manual focus) with 20 or 25mm macro extension tube at f11. EOS 7D at ISO 400, 1/400 shutter speed. Handheld, available light.
Your camera has one really handy feature... That articulated LCD screen should be helpful, shooting macro at odd angles, along with Live View.
There are many other macro techniques... more than it's practical to post about here. If macro photography really interests you, I'd recommend getting some books on the subject and start reading. John Shaw's "Close-Ups in Nature" is a good starting point, but I've read other helpful books by Tim Fitzharris, Joe and Mary MacDonald, Nial Benvie, George Lepp, Heather Angel and others. Head on over to Amazon and do a search.
Macro photography isn't easy... Heck, if it were everyone would be doing it!
Look at your subject and see if you can arrange the plane of focus parallel to their body or otherwise, to have adequate depth of field...