The most important things to look for in travel containers are:
1) Size. No larger than 3.4 oz if you’re flying in the United States
2) Leak proof. You don’t want to arrive at your destination and open your bag to find your clothes and electronics covered in Woolite.
My personal preference is Nalgene. They sell sets of travel containers such as my personal stash pictured below:
The ones that are especially useful are the guys with the white and blue caps. Each of those holds 2 fluid ounces and is perfect for transporting our extremely important Woolite. The container with the green cap is too large for a carry on bag, but it makes a great flask so hold onto it in case you need it later.
These containers are sturdy, and they’ve never leaked on me once in years of use. You can find these easily on Nalgene’s website and also at several online retailers like Amazon.
Nalgene sells a handful of sets with different combinations of bottle sizes. I bought the medium travel kit, but it also comes in a small version and a TSA compliant version with a bag. For most travels less than 2 weeks in duration, any of the kits will have enough volume to hold the amount of Woolite you need for one person.
Just like everything else I recommend, these are pricier than what you’ll find at the dollar store or discount warehouse. But you’ll likely only need to buy them once.