
Sorry but --- dont be silly!
IF you had a really good reason for this, ie you wanted a good all round working dog, small in size, fast and capable of water retrieval as well as running/bushing etc then perhaps you would have a point. If you had a waiting list of people for one of these pups... if you were asking for a stud dog that had a reputation as a good worker...
You have NONE of these things AND you are wanting to cross a dog who is already of a type that can be found quite easily. Most beddy x whippets look IDENTICAL so you cant claim they are hard to find, they vary too much etc etc, the fact is, they DONT.
Asides taht, once you introduce a third breed you dont know WHAT you will get.
Genetics does NOT give you an equal third of each dogs characteristics (or even 25% beddy, 25% whippet, 50% poodle).
In REALITY, (that place where bleedin thousands of crossbreeds are dying everyday because there arent, and never will be, enough homes for them all), thats just NOT what happens.
In reality, you get a litter, say its a litter of 6 pups. Two might look like taller skinnier poodles, two might be smooth coated, two might look just like poodles. BUT none look like your bitch.
Or, you could get a bolshy opinionated dog with all the WORST traits of each (and imho, mini poodles can be very bolshy little things as can beddies who are also not shy of a fight and if yours was working bred then it WONT be!, and whippets (again yours will be part working bred whippet) are likewise not shy of a scrap if needs be and bleeding fast with it.
What a nightmare!!!
Thats on top of the massive costs, the risks to your bitches health and then the work involved finding homes for them all.
Go to a rescue, get a beddy x whippet dog!
Em