$100 · Kitten for rehoming

Found this kitten abandoned and I've been raising it for the past 3 weeks. It's still very small so I would say it wouldn't be older than 10 weeks. I really wish I could keep it but I have a 3 year old dachshund and a 2 year old Tabby female. The kitten loves my dog and wants badly to be friendly with my cat but my cat is very territorial so I'm looking to find this baby a new home. I can't quite tell if it's male or female, (ive been calling it Bean lol) but if I had to make a guess based on looking at genitalia and attitude I would say female. Bean is very timid at first as I assume it didn't have the easiest life until I found it. It really loves cuddling in your neck and gets extremely purry and kneads when you pet it. It is fully litter trained, and eats both wet and dry food. Please tell me a little about yourself and the environment Bean would be living in. I really want it to go to a loving home and would be broken to see it end up at the SPCA. Again, I wish I could this baby but I have to choose to keep my 2 year old cat or this one, and I couldn't fathom giving away my cat.