How can I get iOS7 on my iPhone 3GS
There was a project for the iPhone 2G and iPhone 3G as well as the iPod 1G and 2G MB/MC called the WhiteDoor project, it was a custom firmware for the original iPhone that was designed to update the graphics, backport several features of newer iOS versions, and generally increase the scope of capability for the original iPhone so that it could still be used with modern apps and features.

It would seem that this project, called BlackDoor is the same idea as the WhiteDoor firmware, but designed for newer outdated iPhones (model 3GS is supported whereas WhiteDoor only supports up to the 3G.)

BlackDoor firmware comes pre jailbroken, and has both Cydia, Installous, and IPA Installer by default. You may be able to find a modern copy of WhatsApp that is compatible with your model of iPhone on Cydia, as I know software is often maintained for older devices on there. Alternatively you should be able to install an older version of WhatsApp that is compatible with your device through Installous, or directly through IPA Installer if you can find the IPA (iPhone Application file) for an older version of it.

In any event it would seem like a jailbreak would be the best bet for you going forward in general, given how long it has been since Apple dropped support for the iPhone 3GS it is pretty much the only way you will be able to get ahold of and install apps who have dropped support for iOS 6, or use any features exclusive to newer versions of iOS without buying a new iPhone. 

Options for jailbreaking include using the Evad3rs method (probably the easiest for someone new to jailbreaking, and will keep all of your data, a quick search should provide all needed info.), backing up your data and installing the BlackDoor firmware (as previously mentioned it comes pre-jailbroken, info about it, instructions on how to install it, and downloads for it can be found here BlackDoor website). Be aware that if you intend to install BlackDoor it is based on iOS 3.1.3 so it will be a substantial downgrade, only use this if you aren't comfortable with jailbreaking your iPhone yourself.

Finally there is always the option of downloading a copy of the newest version of iOS 6 (6.1.2), opening it, injecting the jailbreak files, and required SHSH Blobs, creating a new custom firmware from the modified copy, signing it with a signature spoofing program like iFaith and manually installing it by putting the iPhone in DFU mode.

Obviously the last option is the most involved and I do not recommend attempting it unless you have a substantial amount of experience with jailbreaking iDevices. In any event though even if you can find an older copy of WhatsApp you will not be able to install it unless the device is jailbroken, as a jailbreak is required to install software without using the AppStore. Ultimately the Evad3rs method is probably the best option for you, and you can find it here if you are interested. Evasi0n.com