Can't believe I only just now noticed!

Dr Winterbourne

Time Turners
I thought that the dog bisciuts may not be to Fluffy's liking, but that's just the sort of thing Hagrid would give a 'dog'.

It could be though, that this was a cunning clue, laid by Dumbledore, in Hagrid's pocket, for Harry. Dumbledore knows Hagrid, knows his weaknesses surely, and probably was sowing seeds, seeing if Harry would draw conclusions, hoping Hagrid would drop hints accidentally (I shouldna said that..) that would lead Harry to the Philosopher's Stone, lead him to Voldemorte.

Also, knowing Hagrids weakness for strays, giving them one day together, Dumbledore could orchestrate a lifelong friendship, and give Harry initial ties to the Order.