Buying a dog/puppy for your daughter is a very big decision. You have to consider many things before you decide on something.

We have got a Shiranian (ShihTzu+Pom) for our 3yr old son, believe it was a very good decision, both are very good pals now.

Factors:
How old is your daughter?
If she is below 5 years, make sure she have a toy group, very quiet and playful puppy. If she is bigger may be you can get a bigger one. Because size and attitude of dog will matter

Is your daughter asthmatic or ill constantly?
Get low shedding or no shedding dogs.

Is she ready for responsibilities?
Can she clean, groom your pet. If not, you should be ready to do it for her, so that she doesnot feel distant from her pet.

Flat?
Staying in a flat, then you have to definitely get a quieter dog so that your neighbours dont complaint against you and regarding toilet training you dont have to worry, it will be tough initially but be persistent and you can work it out. Use a crate initially to keep your pet and take him out for walks.

Buying from Souq Waqif or any other pet shops?
No, I will not support it. We had gone to QAWS, yes there were very nice dogs for adoption, but nothing was suitable for my 3yr old, so we waited and waited till we got LUCKY which we had adopted from a family. I suggest you wait and keep checking QL consistently, you will get one. Recently I saw a ShihTzu for good home and a Chihuahua for Qrs,900/- only. These are from homes, so there is a 70% chance it will be healthy and good for your daughter.

Finally, did you test your daughter's likeness?
Try taking her to QAWS or to someone with smaller breeds and see how she reacts to them. If she is fine with it then you can go ahead with your decision.

Believe me a dog/puppy is a very good decision for a pet and it is never a big issue, if you do the selection very carefully your pet will be a member of your family otherwise it can be a burden.

Sorry for such a looooooong answer, but take time to select your daughter's pet, afterall its for your daughter.