Age 3 is a funny age, they are starting to get a little too old for the pre-school Jo Jingles classes but are too young for activities like choirs and singing groups.
For the moment I would try her with something like Jo Jingles, then if she enjoys it but begins to outgrow it, move her at age 4/5 into something like Stagecoach.
Do NOT even consider private one to one singing lessons until at least age 9/10 (for some children even that is too young. You have to be so careful with young voices. They should be doing posture, breath control, intonation and learning a variety of appropriate styles in group singing lessons but one to one are too intense at that age.
From about 7 or 8 onwards you can look into junior choirs. The LEA may have one.
Activities you can do yourself include things like pitch matching. Sing a note and get her to find that note, then move your voice up or down a bit so she follows the note.
Sing lots of songs with her, don't worry about it being "right" just foster enjoyment.
We do little warm up excercises with our children, singing me ah smile up the scale for example but she may be a little young for that.
(my dh is a singing teacher by the way)