Toonstruck comes on GOG prepacked with ScummVM but there is a simple (and legal) way to play it in DOSBox.
First, game lacks file DOS4GW.EXE which can be found in many other DOS games from GOG, in my case it was Mortal Kombat. Just copy the file to MISC folder.
Next we have to create a configuration file, so open Windows Notepad (or similar program) and paste the text below:

[TOONSTRUCK]
CD = D:\

[CD]
TransferRate = 3472590

[CPU]
CPUID = Pentium

[DIGITAL]
DeviceName = Sound Blaster 16/AWE32
DeviceIRQ = 5
DeviceDMA = 5
DevicePort = 0x220
DeviceID = 0xe018
DeviceMonoID = 0xe017
Stereo = 0
TimerRate = 60
Flip = 0

[VIDEO]
UniVBE = 1
Width = 640
Height = 400
PaletteWidth = 8
Linear = 1

Save the file as TOONSTRK.CFG and place it in the MISC folder.

Now the only thing that's left is to mount game folder in DOSBox, preferably using dedicated dosbox.cfg file. So if the game is install on C drive it should look something like this:

[autoexec]
# Lines in this section will be run at startup.
# You can put your MOUNT lines here.

mount c "C:\Toonstruck\Toonstruck"
mount d "C:\Toonstruck\Toonstruck" -t cdrom
C:
cd MISC
toonstrk.bat
exit

That's it. I didn't test it to the end but it plays into and game should work. The only problem I have vs running it in ScummVM is that the intro have scanlines as if hardware was insufficient to play them in best quality. I didn't fount solution for that yet. Rest of the cutscenes plays without scanlines.