Wish I could simply say yes or no but not as easy as that.
1) Many pre-1960 houses have no earth to lights and need re-wiring if yours is one of these then it's a non starter.
2) The idea of separate circuits is that should something go wrong with TV it would not fuse the lights there has to be some consideration of over load as well.
3) Lighting circuits are normally just 5 or 6 amp where power circuits are between 16 and 32 amp it depends on the load already on the circuit and in theroy you should not fit a 13A socket to a lighting circuit because something else may get plugged in.
So general answer is no you should not use it. However many wall lamps are in fact powered from the power circuits through a fused connection unit. You can also use a FCU to limit the load which can be drawn so with a 6 amp lighting circuit using a FCU with a 2A fuse would reduce the chance of other equipment plugged in causing the lights to fail.
When looking at the power circuit we also have problems. In the UK we use the ring final system and two cables rated at 20 amp feed the sockets from a 30A fuse or 32A MCB. We are permitted to take one un-fused spur from any socket to feed an outlet device be it a single socket, double socket or FCU. But in many houses these rules have not been followed.
With a 16 or 20 amp fuse/MCB then there is not the same problem.
We also now have new rules and although you can use existing sockets any new ones must follow the new rules. This means any new socket or cable buried in the wall needs RCD protection. In many old houses it means before any new sockets are added the fuse box or consumer unit needs changing for a new consumer unit with RCD protection built in.
So must depends on your existing system. You say little girl so having RCD protection is really something you will want if not already installed. At the end of this year new rules are due to come in which will raise the price by a huge amount all new consumer units from next year will need to be steel so it would make sense to get it changed before the price goes up. Steel is to reduce fire problems when people leave screws loose but clearly an electrician should not leave any loose screws.
With shuttered sockets and RCD protection our system is one of the safest in the world however you would not believe how many people shove in silly bits of plastic into the sockets defeating the protection. In Germany for example they don't have shutters and also no fuses in plug and reversible plugs with some times no earth so for them the idea of plastic covers may make some sense but that's not the case in the UK. (See fatefully flawed
http://www.fatallyflawed.org.uk/)
But first thing it to find out what the light is fed from it may be it's already from the power circuit. Then inspect the fuse box/consumer unit and see if already RCD protected. Using a RCD FCU maybe you can still add a socket.
The point is also of course you can break all the rules and do anything you like and unless some one is injured your unlikely to get caught. But the whole idea is to make it safe for your daughter so you have to do a risk assessment. Any electrics altered should be tested and if you followed rules to the letter then there would be no DIY on electrics as the test gear costs so much. Clearly people do DIY and so one has to decide how far to go breaking the rules. We all do it I will often drive at 75 on a motorway but would not drive at 100 it's a case of risk assessment.
There are plug in testers with loop test at around £50 and personally I think that's a reasonable cost to test sockets. There are those without loop test at around £10 personally I don't think they are good enough. You have to decide how much DIY are you likely to do and should you get a Martindale EZ150 tester or is it better to get an electrician to do the job.
On the forums there is often a question should we say yes or no when we get the question "can I" in the main if following regulations to letter answer is no. But few follow regulations to the letter. So what I feel is if likely safe then go ahead. My house has an emergency light at top of stairs to see way down with power cut so if something trips my lights there is no real danger.
So do that risk assessment.
