In general, if I have to do some levelling of pets, in Legion, I end up going to Val'sharah up and down the road ... though you might get tired of Gleamhoof's. After that, the area around the road in High Mountain from Witchwood, is just full of rabbits and other easy pets to take down, and level your characters in the middle. Stroheim along the road near Valdisdal is also a good area and fairly safe.
For me, this area is only good to level the pets closer to 25 (I do 20's and up. 18 and 19 fine, but you have to be careful in choosing the spots!), and I don't recall doing any lower levels in Legion at all. Mostly I do 1-5 in Orgrimmar, 6 to 8 in the North Barrens, and then Ashlei, and from then on mostly stones until near the top. But when Squirt is on, it's an easy 10 levels from 1, and it's faster all around.
But, try to center things around the monthly (bi-monthly I think, don't remember!) and Squirt as much as possible. You can easily do 500 levels in one day with her, whereas with your daily battles, even if 10 or 15 pet battles, you will only get about 10 levels at best, with some of the extras involved. While that can take 3 or 4 hours, in the end, it's a lot less than you will spend otherwise with the exception that you did it all in one evening or afternoon or morning.
AND, at the very least ... the Safari Hat is a must, even though it's only 10%. Think about it ... that's like 2+ levels every 25.
Hope this helps