Hawks will make the trip to National League side Torquay United later this month for the right to reach the first round proper for the second season in succession.
Doswell acknowledged his troops – including ex-Torquay defender Joe Oastler - face a steep order if they are to come through the fourth round qualifying tie against a side sitting 13th in the division above them.
But the Hawks boss says the FA Cup tie provides a chance for his players to face a team from a level they aspire to be at.
And they'll also have the added carrot of potentially setting up a meeting with League One heavyweights Pompey, Sunderland, Ipswich or Sheffield Wednesday if they are able to spring a surprise with third and fourth tier clubs entering the competition at the next stage.
Doswell said: 'It's one of the toughests draws we could have had, especially being away from home. It's a long way down there as well so it's quite costly with a coach and an overnight stay to do it.
'We aspire to play in the National League, that's what we want to do, they're the sort of sides we want to compete against.
'I'm looking forward to it, it's a chance for us to get together, which we don't usually do, and go down and hopefully put on a good performance, hopefully get a good result, and test ourselves to see where we are as a group against a very good side.'
Gary Johnson's Gulls finished second in the National League last term, suffering the heartache of a play-off final defeat to Hartlepool on penalties at Bristol City’s Ashton Gate. That was after Torquay keeper Lucas Covolan, now at Port Vale, had headed a 90th minute equaliser to force extra time.
Doswell says the Devonians, who dropped out of the Football League in 2014, have everything in place to be a League Two team.
He added: 'It hasn't been kind the draw - it's only a good draw if you get through and it's only a bad draw if you lose. Certainly, from a football perspective, we'll enjoy it because it's a really good ground. They were very, very close to getting promoted into League Two last season, they've got a League Two set up, League Two pitch and League Two support.
'From our point of view it couldn't have been any tougher, but sometimes I like those sort of games as well, it is what it is.'
Torquay, who the Hawks have never played before, lost their first three home National League games of the season to Altrincham (1-3), Woking (0-4) and Grimsby (1-3). But they thrashed Wealdstone 5-0 at the weekend with two goals from ex-Cheltenham striker Dan Holman.
Hawks will be aiming to reach the first round proper for the ninth time since the club were formed 23 years ago.