I graduated a couple of years ago now, but I went into the course only wanting to work with kids - we had to do one "big" placement with adults one year, and the following year with kids - or vice versa (half did one first, half did the other)... my adult placement changed my mind completely, so it's good the course skilled me for all of it really and I now work with adults and have no intention of switching over!
When it comes up to job hunting you just apply for roles that match up - so some of my course went off to work with paediatrics and some went off into various adult services, and then it tends to be as you move up the bandings you specialise more and more into specific areas. Tends to be very clear in job descriptions what client group you're going to be working with as well.
Two things I'll mention - remember SLT covers dysphagia (swallowing) work as well - it can be a big (or only) part of some roles - some people really hate it, some people love it and some people (I'm like this one) are getting their heads around it and building up confidence more and more and kind of starting to like it.... and lots of paediatric work these days tends to be in blocks of approximately 6 sessions, and much more developing programmes and working indirectly teaching parents and school staff to deliver therapy, rather than working directly 1:1 with kids for weeks on end (unless you go into working in special schools).