Get a djembe instead and find out if your kid has rhythm.

I think you chose the wrong way to respond to the help you came here seeking.
If you're going to be selective about the advice you're willing to accept, you may as well just be deciding on your own.

The advice you have been given is simple and correct. Buy what you are comfortable paying for, but don't worry about quality this early in the game, as it will not matter. If your entire goal is to buy the best quality kiddie kit for your 3 year old, you obviously care more about irrelevant factors than simply providing a means for your kid to decide to enjoy. If you absolutely need the drums to be the best possible brand, that quite obviously speaks more to your own desire than your kid's or the practicality of the matter.
But hey, don't take my word for it. Instead, just think whatever you want to. You obviously have it all covered.

I don't NEED the drums to be the best possible brand...!! I am simply asking advice on a good brand that is not too costly... I am asking because I am ordering from Australia via Amazon in the States so I am not familiar with many of these brands, nor is one of my drummer friends... We only know of the more expensive, known brands so I am trying to avoid those but asking re the brands we have not heard of which are also the cheaper ones...

Thanx Secede, we do have Bongo drums - she also drums on a kids plastic Wiggles drum, a tamborine, her toy Elmo's drums and biscuit tins... She drums on anything and everything including our dogs...!! She is showing great rhythm in her drumming, dancing and loves to sing also - she sings TOMORROW from ANNIE at the top of her voice and loves all musicals, and also loves the Celtic Women DVDs and requests we put them on... I am not trying to enforce anything on her, I am simply trying to encourage the things that give her joy... If she chooses to go further with anything that is her choice to make... I was selected as a New Zealand promising player in hockey when I was twelve - I was also encouraged but not enforced... I did not pursue playing at that level but I continued to play hockey at representative level until I was 18 and socially until I was 21 went travelling - I did not push further through my own choice... I bring my own child up in the same way...

Are there no kiddie kits in Australia? There's got to be a few music shops out there where you can find and demo a kiddie kit. In fact, I think that might be the best route to go, because then you can actually feel them out for yourself and also avoid shipping charges.

Is there any reason you need to order on the net? I still wonder about the need to know branding information if you're not concerned with quality. Why not just get whatever is in your price range and is reviewed well? Your kid won't mind.

Thank you Freebase Dali, yes there maybe somewhere I could find a demo kids kit - I need to look further and if/when we do a trip to the city... We live in a small town in remote Western Australia, we are a 2400km round trip drive to the city, Perth... hence ordering online and Amazon have free shipping... basically most shopping by all residents here is done online & unfortunately you have many experiences of buying things that look authentic and good but when they come you have been either lied to or shafted or you are unable to view well what you are buying - hence why I am asking reputable kits... It is not so much brand name I am after - I am not a brand basher by any means... I just like to know if I am buying something decent that is not going to fall apart and that theory stands for anything I am purchasing... Sometimes you go the cheaper option and in a week it breaks and when if you paid slightly more you get a better product that last... Unfortunately due to isolation we often have to purchase this way... I will do some more research re reviews, I guess it is reviews I came here for...