Generally speaking aftermarket magazine don't work very well, but you might get an exception. If necessary, order one - and if it works order a second.
Original magazines sometimes turn up, but are costly. Beware of cracked lips.
One other thing. Most of Browning's designs were well thought out, but this one has a flaw. The firing pin has a long nose, which also acts as the ejector. When ejecting fired cases there isn't any problem, but when you eject a loaded round the firing pin/ejector will hit the primer dead center while the case is halfway pulled out of the chamber.
So if you have to eject a live round, first remove the magazine and then
pull the slide back gently. The round will usually tumble down the magazine well. Practice with a dummy round or fired case, and don't dry fire without a fired case in the chamber. Otherwise you may break off that long firing pin nose.
Other then this issue you have a fine little gun.
Oh... and no. The Baby Browning magazines won't work, but those made for the Browning model 1906 Vest Pocket Model will. For a magazine try:
www.e-gunparts.com But unless you specify "Colt original" you'll get an aftermarket magazine of questionable quality.