Can someone spy on my iPad using peektab or other spy apps?

Is your iPad jailbroken? If it isn't then Peektab, and most if not all monitoring software of that nature, cannot be installed.

If it is Jailbroken, then we cannot help you as Jailbreaking is not supported by Apple, and as such forefits any help from them or these forums.

Why do you tihnk it has been installed? If its a corporate tablet, then the company is entitled to install whatever they deem necessarry on their devices.

In order to install it on your daughter's iPad, you would need to jailbreak it. This is NOT recommended. It will make the device less stable, vulnerable to malware and void the warranty. And, despite what the Peektab website says, this is not always easily undone.

Not unless you jailbreak it.

An un broken iOS, does not allow apps access to other apps activity or file area as by designed all Apps are kept in their own sandboxed areas without no access to other Apps, or the system itself.

Jailbreaking allows Apps to go and access anything they want anywhere on the device, which not only allows monitoring software to run, but exposes the iPad to viruses and other nasty things they are otherwise not vulnerable to.