ASP.Net Core API bind model int Ids to custom Id objects

I have structs which represents Id's for different types. That structs have int property "Id", public constructor with (int id) parameter and implements IEquatable interface. I want my ASP.Net Core WebAPI application to somehow bind those structs to incoming integer Ids in query. I know that there are custom model binders, but to use it I need to implement custom model binders for all query models, because marking each key-struct property with custom model binder not enough - I need to register custom model binder provider, where I switch ModelType and return single model binder, like so:

    public class CustomModelBinderProvider : IModelBinderProvider
    {
        public IModelBinder GetBinder(ModelBinderProviderContext context)
        {
            if (context == null)
            {
                throw new ArgumentNullException(nameof(context));
            }

            if (context.Metadata.ModelType == typeof(DogQueryModel))
            {
                return new BinderTypeModelBinder(typeof(DogQueryModelBinder));
            }

So I can't create just one model binder for each Id struct - need to create it for each query model.

To make it clear I will provide some example code of that struct, query model and action:

    public struct DogKey : IEquatable<DogKey>
    {
        public DogKey(int id)
        {
            Id = id;
        }

        public int Id { get; }

        #region IEquatable implementation
        #endregion IEquatable implementation
    }

    public class DogQueryModel
    {
        public DogKey Id { get; set; }
        public SomeOtherKey OtherId { get; set; }
        public string Name { get; set; }
    }

    [HttpGet("dog")]
    public async Task<ActionResult<IList<DogResultModel>>> GetDogs([FromQuery]DogQueryModel dogQueryModel)
    {
        //use dogQueryModel.Id as DogKey struct
    }

I want to query it like this: https://localhost/api/v1/dogs/dog?id=1&otherId=2&Name=dogname