It is possible in general, although a Bluetooth dongle may support only a subset of Bluetooth profiles.
I think keyboards operate on an HID profile, while speakers require A2DP. So you may or may not be able to use speakers with your specific dongle, depending on what profiles it supports.
You should try to pair your speakers with the dongle in the same way you have paired your keyboard and in the same way you have paired your speakers elsewhere. Have in mind that successful pairing may happen even if the dongle lacks support for required profile.
You have paired your keyboard at least once? Or haven't you?
In case you never had to pair your keyboard with the dongle, there comes another issue: are you sure you've got a Bluetooth keyboard, not a simple wireless one? It's good if you are sure, but certainly there are users out there who do not know the difference, so let me explain for them.
As far as I know, vast majority of wireless keyboards and mice uses non-Bluetooth (vendor-specific, I think) protocols to communicate with their dongles. The reasons are: lower power consumption and simplicity. Such a set works "out of the box", the keyboard knows nothing about relatively complex Bluetooth, pairing, etc. The host may also know nothing about Bluetooth, and USB support is enough.
In addition, there isn't any need for two-way communication: the keyboard works as sender only, and the dongle as a receiver; still, Bluetooth requires two-way communication, even with a keyboard or mouse. That's why Bluetooth devices are more expensive than their non-Bluetooth counterparts.
Bluetooth or not, how can you tell? A Bluetooth keyboard should have a Bluetooth symbol on it and a button allowing it to pair with something other than attached dongle (example: with a laptop having internal Bluetooth adapter).
In fact, there isn't often any dongle in the set. The Bluetooth dongle reports to operating system as Bluetooth radio, while non-Bluetooth keyboard dongle is recognized directly as a keyboard (HID device) connected to USB just like any wired USB keyboard.
If your keyboard and dongle are Bluetooth devices, you have to pair them in every operating system you connect the dongle to, because a Bluetooth keyboard (and any other Bluetooth device) pairs with the operating system via the dongle, not with the dongle only. If given set works just by plugging the dongle, then it's not Bluetooth.
In case you cannot tell whether you've got Bluetooth or non-Bluetooth keyboard, name its model here, so we could figure it out. If it is Bluetooth one and you need more help pairing speakers, I need to know your operating system before I guide you further.