It would be a perfectly reasonable thing to do. Easy and cheap. I've
done it myself a week or two ago and I was surprised how painless it
was. These things are remarkably similar across brands so here's what
I would recommend based on my Creda:

Switch it off at the consumer unit and the wall switch (better safe
than sorrry).
Remove the hob from the worktop. It's probably held in by a couple of
brackets from underneath.
Keeping it the normal way up (important) remove all of the screws
around the side and prise off the controls. Lift away the glass top.
The elements are probably just resting in place on springy holders.
Look underneath the dead one and record any markings. Measure its
diameter and note its power rating.
As a check take a resistance measurment on the suspect element, it
should be between 30 and 50 Ohms if it's good and infinite if it's
dead.
If you're lucky the manufacturer will be knowledgable and helpful and
will supply you a new part for a reasonable price. Stop laughing,
Creda were exactly that. I quoted the 10 year old model number and
told them which ring it was. They supplied the replacement for £34
which was £6 less than any other supplier I could find except for one
guy on ebay. Admitedly the part I needed was a "solarglow" not a
halogen but in my research I came across lots of them too and none were
more than about £60.
If the hob manufacturer can't or won't help there are plenty of second
sources and it appears there are only a very small number (like two or
three, Solarspeed in the Midlands and Eika in Spain are the only ones I
found) companies who actually make the elements anyway and even then
they are interchangable in many cases. If you've got anything fancy
like "hob hot" indications make sure you get an element which supports
this too.
When you get the new element you will need to transfer the mounting
tabs from the old one, making sure you get them in the same positions.
Then, as they say in all the good manuals "reassembly is the reverse of
removal" and in this case it's true but you also need to add the steps
of admiring your work and congratulating yourself on how much you've
saved over getting an engineer out.

Good luck,
Calvin